tag:blogger.com,1999:blog-3221050996555608372017-07-18T21:50:29.494-07:00PRIME Time Math PUSDDuane Habeckernoreply@blogger.comBlogger141125tag:blogger.com,1999:blog-322105099655560837.post-74462113657928584362017-07-18T21:50:00.001-07:002017-07-18T21:50:29.539-07:00A Florida school district is banning homework — and replacing it with this<img src="http://ift.tt/eA8V8J" width="250px" height="250px" /><br /><br />Elementary school students in one Florida school district are going to find a welcome new - but controversial - policy when they return to school for the 2017-18 school year next month: no traditional homework.<br /><br />Read more via <a href="http://ift.tt/2vAvIYJ">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-33055805354521329932017-06-30T07:44:00.001-07:002017-06-30T07:44:25.629-07:00David Wees on Twitter<img src="http://ift.tt/eA8V8J" width="250px" height="250px" /><br /><br />Reading: Effective Teacher Professional Development from @LDH_ed http://ift.tt/2sZ3Krm.<br /><br />Read more via <a href="https://twitter.com/davidwees/status/880782484912222210">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-18578051808821512152017-03-02T17:56:00.001-08:002017-03-02T17:56:23.680-08:00What happened when one school banned homework — and asked kids to read and play instead<img src="http://ift.tt/2lJoIGZ" width="250px" height="250px" /><br /><br />Mark Trifilio, principal of the public pre-K-5th grade Orchard School in Vermont, sat down with the school’s 40 educators last summer to discuss the soon-to-start new school year and homework — how much kids were getting and whether it was helping them learn.<br /><br />Read more via <a href="http://ift.tt/2lYWyZs">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-17408271880219098912017-02-28T18:57:00.003-08:002017-02-28T18:57:39.546-08:00Scaffolding word problems<br /><div class="separator" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: left;"><img border="0" src="https://4.bp.blogspot.com/-0Ncn_aTymQs/WLYhZIxpcQI/AAAAAAAAcQo/xRbuy-FXeeQQiKr69dcgHLe92QSZxnSmwCEw/s1600/wordproblemMeme.jpg" /></div><br />Word problems...ugh.<br /><br />Of course we all know the trope: students can't do them, students hate them, blah, blah, blah.<br /><br />Today I had a couple of very sincere teachers asking me how to help some of their students who are struggling with word problems. I did my best, but really I was just doing a bunch of hand waving and using big words like "pedagogy", "schema", and "comprehension". The truth is I wasn't entirely sure how to scaffold word problems for struggling students.<br /><br /> I perused my Google Drive looking for ideas and found these gems, so I thought I'd share them.<br /><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><span style="border-color: black; border-image: initial; margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/document/d/1D9wyHhUTmVCJLoS6ifUQ4MnJkeVEP6j7NM9NzsijIL8/edit" target="_blank"><img height="320" src="https://4.bp.blogspot.com/-8BT7ok98-y8/WLYhS40WnNI/AAAAAAAAcQk/mZos_gQi72kKtki-er9wtulkLIwU8XfgwCEw/s320/page%2B1-1%2B%2528dragged%2529.png" style="border: 1px solid black;" width="247" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/document/d/1D9wyHhUTmVCJLoS6ifUQ4MnJkeVEP6j7NM9NzsijIL8/edit" target="_blank">Click to view the Google doc</a></td></tr></tbody></table><h3>The 8-Step process for drawing the bar model for word problems</h3>I got this many years ago at a Singapore Math training and often find myself reciting it as a mantra while I'm trying to solve a word problem. Interestingly, the same 8 steps are mentioned in <a href="http://embarc.online/course/view.php?id=24" target="_blank">Eureka Math Grade 1 Module 6 Lesson 1</a>.<br /><br /><b>The 8-Steps of Model Drawing </b><br />1. Read the entire problem.<br />2. Turn the question into a sentence with a space for the answer.<br />3. Determine who and what is involved in the problem.<br />4. Draw unit bars of equal length.<br />5. Re-read each sentence one at a time and revise the bar(s).<br />6. Put the question mark in place.<br />7. Work computations to the side.<br />8. Write down your answer to the problem.<br /><br />Step 2 is really important because it verifies early in the problem-solving process whether the student even understands what he is trying to find.<br /><br />Step 4 is surprisingly important. By starting with bars that are of equal length, the act of modifying the bars in Step 5 provides clues as to what kinds of math will be used to solve the problem. Resist the common urge to skip Step 4 and jump straight to creating the drawing! Once the model is accurately drawn, the necessary calculations practically leap off the page.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://docs.google.com/document/d/1D9wyHhUTmVCJLoS6ifUQ4MnJkeVEP6j7NM9NzsijIL8/edit" target="_blank"><img height="400" src="https://4.bp.blogspot.com/-YHp1M3-ra08/WLYhVfn8JeI/AAAAAAAAcQk/HRThYPtO_M8ZtEVJP28KTMwvBSmLgLZZwCEw/s400/page2.png" style="margin-left: auto; margin-right: auto;" width="308" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/document/d/1D9wyHhUTmVCJLoS6ifUQ4MnJkeVEP6j7NM9NzsijIL8/edit" target="_blank">Click to view</a></td></tr></tbody></table><b>How would this look for a 2nd grade problem? Check it out...</b><br /><i>Brienne has 23 fewer pennies than Alonzo. Alonzo has 45 pennies. How many pennies do Alonzo and Brienne have altogether?</i><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lzxo-fiPueI/WLY2--HDxqI/AAAAAAAAcQw/L1QArn0sTx0Kr_n2b5SQCQSe_9lN_EwVgCLcB/s1600/example.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="195" src="https://3.bp.blogspot.com/-lzxo-fiPueI/WLY2--HDxqI/AAAAAAAAcQw/L1QArn0sTx0Kr_n2b5SQCQSe_9lN_EwVgCLcB/s400/example.png" width="400" /></a></div><br /><br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><span style="border-color: black; border-image: initial; clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/document/d/1b2mIq7Wh4PqMkfMVnD0BoNVvF_2FfPmfM6rJWL1Am_Y/edit" target="_blank"><img height="320" src="https://4.bp.blogspot.com/-BL-jbH5BvGo/WLYhXX0jtiI/AAAAAAAAcQk/zN200j75kPcOrvmcIvA-61iDfDO4l-e5QCEw/s320/page3.png" style="border: 2px solid black;" width="266" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/document/d/1b2mIq7Wh4PqMkfMVnD0BoNVvF_2FfPmfM6rJWL1Am_Y/edit" target="_blank">Click to view</a></td></tr></tbody></table><h3>A graphic organizer</h3>Long ago I was given a graphic organizer that accompanies the 8-steps. I modified it so that teachers can give the struggling student a sheet for each problem to be solved. The problem goes at the top and then there are work spaces provided along with the 8 steps explicitly listed along side.<br /><br /><h3>What I've learned</h3>Far more important than the calculations is the model drawing. Spend far more time with your struggling students on the model drawing, since it is far more important than the actual calculations. Once the model is drawn, some students will use subtraction to solve the problem, while other students will solve the exact same problem using addition. Using the drawn model to understand the problem is far more profound than simply teaching students to look for key words.<br /><br /><b>In a nutshell:</b><br />Key words? Not good enough.<br />Drawing a model? Good!<br />.<br />.<br />.<br /><br /><br /><br /><br /><br /><br /></div><br />Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-52430779376202357102017-01-26T09:38:00.002-08:002017-01-26T09:38:40.958-08:00Rethinking Homework<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-9VVBp4EgbK4/WIoyF6p04aI/AAAAAAAAa3g/6vEARczAis0qjoYGqYckv7ocXifauf6YgCLcB/s1600/NCSM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="63" src="https://1.bp.blogspot.com/-9VVBp4EgbK4/WIoyF6p04aI/AAAAAAAAa3g/6vEARczAis0qjoYGqYckv7ocXifauf6YgCLcB/s400/NCSM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">If you are a mathematics instructional coach then I can't express enough how important it is that you join <a href="https://www.mathedleadership.org/" target="_blank">National Council of Supervisors of Mathematics (NCSM)</a>. A benefit of membership in this fine organization is the Marshall Memo, which is a "weekly round-up of important ideas and research in K-12 education. This alone is worth the cost of membership!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Today in the Marshall Memo is a wonderful summary of an ASCD article about homework. Before you read the summary, please do two things:</div><div class="separator" style="clear: both; text-align: left;">1. Join <a href="https://www.mathedleadership.org/" target="_blank">NCSM</a></div><div class="separator" style="clear: both; text-align: left;">2. Join <a href="http://www.ascd.org/" target="_blank">ASCD</a></div><br />Now, read on...<div>-----------------------------------------------------------------------------<br /><br />(Originally titled “Does Homework Help?”)<br /><br /> In this Education Update article, Alexandria Neason reviews the research on the impact of homework, which is decidedly mixed. One study showed a correlation between completing homework and better scores on unit tests, but the link was weaker in elementary schools. Other studies found no strong evidence of homework leading to higher grades. “We still can’t prove it’s effective,” said education professor Cathy Vatterott, author of a 2009 book on homework. “The research is flawed and idiosyncratic.”<br /><br /> What’s indisputable is that lower-income students find homework a challenge, and not completing homework has a disproportionate impact on their grades. Myron Dueck, a Canadian school leader and author, says one of the most serious effects of homework is “the exacerbation of social and economic inequities that already exist.” Students who are struggling with food insecurity, unstable housing, noisy and distracting home environments, inadequate computer access, after-school jobs or child care, and the normal challenges of adolescence often find homework too much to handle. And indeed, studies of high-school dropouts cite homework as one of the top reasons for throwing in the towel.<br /><br /> Given this gap-widening effect (“We are basically punishing them for their poverty,” says Vatterott) what should schools do? Neason summarizes some possible policy tweaks:<br /><br /> • Beef up the rigor and engagement of in-school lessons so that missing homework takes less of a toll on achievement. One district made a point of including music and sensory objects in heavily scaffolded lessons.<br /><br /> • Give students opportunities to complete homework in school with a conducive study environment and good computer access.<br /><br /> • Use homework to reinforce already-mastered skills or complete assignments that were launched in class rather than introducing new material. “Homework should reinforce students’ confidence in their abilities, not shatter it,” says Neason.<br /><br /> • Don’t assign busywork. Each homework assignment should have a clear rationale and add value.<br /><br /> • Don’t assign homework that requires students to buy special materials like poster board.<br /><br /> • Don’t portray homework as a test of responsibility. Students may be ashamed to tell teachers about out-of-school struggles that make homework difficult for them to complete.<br /><br /> • Rethink the weight of homework on grades. Students might be graded on what they learn rather than on process pieces such as homework assignments. One approach is to make homework optional and check for understanding with a quick quiz the next day.<br /><br /> • Rethink zero-to-100 grading scales, which have a devastating effect when a student gets a zero for missed homework. A 6-5-4-3-2-1 scale mitigates this effect.<br /><br />• A variation on this is limiting homework to 10 percent of students’ grades or giving a grade of incomplete with time to complete it, perhaps during lunch or recess.<br /><br /> • At the elementary level, eliminate homework entirely. Some elementary schools have stopped assigning homework and encourage students to play and read after school.<br /><br /> <br /><br />“Does Homework Help?” by Alexandria Neason in Education Update, January 2017 (Vol. 59, #1, p. 1, 4-5), ASCD member log-in access at <a href="http://bit.ly/2k4lvyc">http://bit.ly/2k4lvyc</a></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-58409743850735610632017-01-09T13:21:00.001-08:002017-01-25T13:15:26.426-08:00Female teachers’ math anxiety affects girls’ math achievement<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-fAWmLe04viw/WHZO5TUpttI/AAAAAAAAaKU/iRoTUfyiZiEfjwmbtSRde5gQ7Q-68MrhgCLcB/s1600/math%2Banxiety.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-fAWmLe04viw/WHZO5TUpttI/AAAAAAAAaKU/iRoTUfyiZiEfjwmbtSRde5gQ7Q-68MrhgCLcB/s1600/math%2Banxiety.jpg" /></a></div><br /><br />People’s fear and anxiety about doing math—over and above actual math ability—can be an impediment to their math achievement.<br /><br />Read more via <a href="http://ift.tt/2ibJ6yT">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-56527664713741563932016-12-13T08:01:00.001-08:002017-05-07T17:16:20.390-07:00Why Kids Should Keep Using Their Fingers to do Math<img height="250px" src="https://ww2.kqed.org/mindshift/wp-content/uploads/sites/23/2016/04/Math-1440x810.jpg" width="250px" /><br /><br />Nearly all kids learn how to count using their fingers. But as kids grow older and math problems become more advanced, the act of counting on fingers is often discouraged or seen as a less intelligent way to think.<br /><br />Read more via <a href="http://ift.tt/2hJq0gx">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-78713170736753039642016-11-06T18:49:00.001-08:002016-11-06T18:49:07.804-08:00A school's "no homework" policy led to kids getting better grades and it's a super inspiring story<img src="http://ift.tt/2fsZbPY" width="250px" height="250px" /><br /><br />In grade school, homework was the bane of our existence. It wasn’t uncommon to glance around to see a classmate working on assignments for other classes during lectures, or to see students hard at work in the library or at the lunch table.<br /><br />Read more via <a href="http://ift.tt/2fsXsKz">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-69638882136903919012016-10-09T12:44:00.001-07:002016-10-09T12:44:33.204-07:00Stop the Homework Insanity and Let Kids Be Kids<img src="http://ift.tt/1PUgXC4" width="250px" height="250px" /><br /><br />I have so many fond memories of my childhood. Growing up in a relatively rural area of Northwestern New Jersey sure had its benefits. As we returned home from school each day, my brothers and I would jump off the bus and diligently make our way about a half-mile back to our house.<br /><br />Read more via <a href="http://ift.tt/2d16G0e">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-84257667913528123542016-10-05T06:30:00.000-07:002017-07-01T09:52:57.966-07:00#EurekaMath: How to pace the lesson and meet the needs of EVERYONE<div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-DM9otQhQpbk/WAgaZaBj1qI/AAAAAAAAXh0/3HFZ5fg2Qbc/s640/blogger-image--1315494094.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="https://lh3.googleusercontent.com/-DM9otQhQpbk/WAgaZaBj1qI/AAAAAAAAXh0/3HFZ5fg2Qbc/s320/blogger-image--1315494094.jpg" width="320" /></a></div>As much as I love the Eureka Math curriculum, teachers seem to have a real tough time figuring out how to pace the lesson while also meeting the needs of all their students. I am finding teachers struggle in this regard with Eureka Math far more than they did with the pre-Common Core textbook. I don't see this as a knock against Eureka Math. If anything, it merely speaks to the cruddy quality of the old textbooks and that the old textbooks were nothing but snake oil, convincing us we were doing a good job, when in reality we weren't.<br /><br />Recently, I received an email that is very typical of teachers new to Eureka Math. Here is the email and my response. I hope it helps someone else out there in Internet-land.<br /><br />----------The original email----------<br /><br /><i><b>Hi Duane,<br /><br />I am an Instructional Coach in the XXXXX School District in Washington state and I hope you don't mind if I ask you a question about Eureka Math. This is our first year of implementation and teachers are really struggling with the differentiation issue- how to meet the needs of the low and high students. I'm wondering if you have found ways to address this issue? <br />Additionally teachers are feeling that there is so much to cover in every lesson and the program moves too quickly- and they want to teach the program 4 days a week and then on the fifth day- spend time reviewing concepts taught or missed. They are also struggling with what to cut out... Any words of advice?</b></i><br /><br /><div>-----------My response--------------</div><div><br /></div>Hi there!<br /><br />Your email is a common one that I get weekly from teachers inside and out of my district! Essentially, you are asking two things:<br />1. How to meet the needs of ALL students?<br />2. How to fit all the components of a lesson into a single 45 minutes math time?<br /><br />I'll start with #2 because it also somewhat addresses #1... <br /><br /><div>In general, I see teachers move through the components of a lesson too slowly. This is because teachers LOVE their students and do not want to move too fast for the struggling students in the class. Unfortunately, this means a fluency activity that should take only 3 minutes ends up taking 10 minutes. Or an Application problem that should take 8 minutes ends up taking 20 minutes because the teacher turned what should merely be a short formative assessment opportunity into a full-on teaching moment. Finally, the teachers often trudge through too much of the Concept Development, doing too many examples at too slow a pace. Or worse, the teacher skips the Concept Development altogether and just works with the whole class in completing the Problem Set questions.<br /><br /><b>What is the result? </b></div><div>The students who understand the math and are ready to move on become bored because the teacher is going too slow. I call this "over teaching". The teacher is teaching too much (trying to help the strugglers) and not letting the top students move to independent work time. Moreover, the low students, for whom the teacher is "over teaching", still aren't understanding the math because what they need is something altogether different - perhaps a small group intervention, reteaching with manipulatives, or back-filling with content from an earlier grade.<br /><br />Here is a blog post I wrote a little while ago that goes more into specifics about how to pace an individual lesson...<br /><a href="http://primetimemathpusd.blogspot.com/2016/08/pacing-with-eureka-math-engageny.html">http://primetimemathpusd.blogspot.com/2016/08/pacing-with-eureka-math-engageny.html</a><br /><br />With proper pacing, much of #1 is addressed automatically. Counterintuitively, the proper pacing is probably faster than what teachers typically do.<br /><br /><b>Now to address #1 a bit more...</b>Let's assume the teacher has kept a zippy pace with the fluency activity and the application problem. Now she is ready to do the Concept Development. This is where I suggest teachers resist the urge to "over teach". The teacher should choose the minimum number of example problems from the Concept Development vignette in the teacher edition and then release most of the students to independently work on the Problem Set, while she immediately works with a few students in a small group setting.<br /><br />Of course, this means the teacher is now doing double duty: 1.) continuing to teach the strugglers in the small group and 2.) monitor the rest of the class to ensure they are working productively. This is hard, but can definitely be done. <br /><br />Keep in mind that the Problem Set is a time-based activity rather than a product-based activity. This means students are working on the Problem Set for a fixed amount of time (about 10 or 15 minutes) regardless of whether they finish all the problems. Indeed, the teacher should identify the problems in the Problem Set as "Must Do", "Could Do", or "Extension". During the 15 minutes, students should first do the Must Do questions, then the Extension Questions. Time permitting, the Could Do questions are last.<br /><br />As students complete the Problem Set, I encourage teachers incorporate some sort of problem-solving opportunity for students to work on. Some awesome online resources:<br /><ul><li><a href="http://www.matific.com/">http://www.matific.com</a></li><li><a href="http://www.openmiddle.com/">http://www.openmiddle.com</a></li><li><a href="http://nrich.maths.org/">http://nrich.maths.org</a></li></ul>These allow students to work on something OTHER than drill-and-kill math. Of course, the teacher can certainly use other problem-solving activities she may already have.<br /><br />Once the teacher finishes working with the strugglers in the small group, often there is no time for those students to work on the Problem Set. This is okay. Just move on and have the students skip the Problem Set that day.<br /><br />The important thing is for the teacher to resist the urge to reteach the entire lesson the next day simply because a few students do not understand today's lesson. The curriculum is specifically written to spiral and review, which makes reteaching rarely necessary.<br /><br /><b>So...let's boil this whole thing into a simple game plan for teaching:</b><br /><ol><li>Properly pace the fluency activity and Application problem. Keep it zippy. Assess student understanding, but don't turn it into a teaching moment.</li><li>Keep the Concept Development to a minimum. Do as few examples as possible in order to release most students as quickly as possible. I call this "UNDER teach" the math...meaning the teacher should send students to work independently a little earlier than she might otherwise have done.</li><li>The teacher now does double duty: reteach a small group while also monitoring the rest of the class.</li><li>Have additional problem-solving activities (online or paper-and-pencil) for early finishers of the Problem Set.</li><li>Limit the Problem Set time to 10 or 15 minutes only. Then do a short Debrief conversation with the whole class.</li></ol></div><div>Sheesh...there is more we could talk about. Specifically, Universal Design for Learning (UDL). This is a framework for how a teacher can design/modify a lesson in order to meet the needs of more students within the lesson, thereby reducing the need to differentiate for the high- and low-students after the lesson. In UDL, teachers proactively plan strategies for removing barriers to student learning in three ways:<br /><ul><li>Strategies for engagement</li><li>Strategies for representation</li><li>Strategies for expression. </li></ul>Here is a good resource for learning more about UDL...<br /><a href="https://goalbookapp.com/toolkit/strategies">https://goalbookapp.com/toolkit/strategies</a><br /><br />I hope this gets you started on your journey. Please feel free to email again. We all need to support one another as we help our teachers implement Eureka Math!<br />.</div><div>.</div><div>.</div><div>.</div><div><br /></div><div><br /><br /><div><br /></div><div><br /></div><div><br /></div></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-71337246783543280412016-09-21T08:53:00.000-07:002016-09-21T08:53:38.391-07:00How to catch up in Eureka Math<div class="separator" style="clear: both; text-align: left;">This weekend I was asked a question via my <a href="http://www.youtube.com/dhabecker" target="_blank">YouTube channel</a>. The question is a common one that I have heard numerous times. It isn't unique to Eureka Math either...I've heard it my entire 26 years of teaching.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Here is a screenshot of the question and my quick response at the time.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-Xa8wAXEkgUI/V-KmJyUNPVI/AAAAAAAAWKA/6ey6z5regZUFwOc2sfeyuDDsZ637dcbawCLcB/s1600/youtube.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="434" src="https://4.bp.blogspot.com/-Xa8wAXEkgUI/V-KmJyUNPVI/AAAAAAAAWKA/6ey6z5regZUFwOc2sfeyuDDsZ637dcbawCLcB/s640/youtube.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">As I reflect on my response, here are some additional thoughts...</div><div class="separator" style="clear: both; text-align: left;"></div><ul><li>The strategy of "catching up" a student by going backwards two years just doesn't make sense to me. Essentially, the strategy is flawed from the start because it takes a student who is already struggling with mathematics and merely piles more math on top of the student. In order for this strategy to work, not only does the struggling student have to learn the current year's standards, but also the standards from the previous year or two. For a student already struggling with math, this is just plain silly.</li><li><a href="http://www.greatminds.org/" target="_blank">Eureka Math</a> (<a href="http://engageny.org/" target="_blank">EngageNY</a>), being OER, affords us the ability to print "just in time" content for a student in need. Rather than subjecting the struggling student to the ENTIRE previous two years' worth of math, let's just print an occasional worksheet from a previous year. The strategy here is to have laser-like purpose for what "old" math to teach the student.</li><li>Most importantly, before we try to "fix" the student, let's first reflect on what went wrong in the first place that caused the student to need fixing? <a href="https://goalbookapp.com/toolkit/strategies" target="_blank">This is UDL</a>!!! Moving forward, how can we select strategies for engagement, representation, and expression that remove the barrier to learning in the first place?</li></ul><div>.</div><div>.</div><div>.</div><div>Just a thought.</div><br /><div class="separator" style="clear: both; text-align: left;"><br /></div><br />Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-28531812814585781762016-09-12T11:44:00.001-07:002016-09-12T11:44:42.787-07:00Research Finds Effects Of Homework On Elementary Students<img src="http://ift.tt/1qBmVmC" width="250px" height="250px" /><br /><br />After over 25 years of studying and analyzing homework, Harris Coopers’ research demonstrates a clear conclusion: homework wrecks elementary school students.<br /><br />Read more via <a href="http://ift.tt/1SiQsaZ">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-47942890130847592732016-09-10T15:09:00.001-07:002016-09-21T08:21:46.268-07:00Are Timed Math Tests Harmful to Students? — MashUp Math<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lM62FkgT--8/V-KlNubWxDI/AAAAAAAAWJ4/GrpeHfq8_GE71hdqKmI-m9wT58sJ1_YDACLcB/s1600/mashup.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="182" src="https://3.bp.blogspot.com/-lM62FkgT--8/V-KlNubWxDI/AAAAAAAAWJ4/GrpeHfq8_GE71hdqKmI-m9wT58sJ1_YDACLcB/s320/mashup.jpeg" width="320" /></a></div><br /><br />Question: Which of these statements best describes an exceptional math student? If you chose one of the first three statements, then your beliefs about the essence of math understanding may be rooted in misconceptions.<br /><br />Read more via <a href="http://ift.tt/2c24XHu">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-17509877510465563512016-09-08T23:09:00.003-07:002016-09-08T23:09:12.960-07:00Why Parents Should Not Make Kids Do Homework<img src="http://ift.tt/1pwaZ5v" width="250px" height="250px" /><br /><br />President Obama’s pick for Education Secretary, John King, Jr., is headed for confirmation Mar. 9. King’s track record shows he loves standardized testing and quantifying learning.<br /><br />Read more via <a href="http://ift.tt/1p5YNrz">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-19331348689812063042016-09-08T23:09:00.001-07:002016-09-08T23:09:11.576-07:00Here’s why I said no to homework for my elementary-aged kids<img src="http://ift.tt/1pyjTQ0" width="250px" height="250px" /><br /><br />Here’s a shocking thought: What if not doing homework was better for your kids? Would you still make them do it? We want what’s best for our children, and when kids hit school age we follow the teacher’s lead. If the teacher assigns homework, we enforce it at home. Even in elementary school.<br /><br />Read more via <a href="http://ift.tt/257In2S">Pocket</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-56439246842230536402016-09-07T17:39:00.000-07:002016-09-07T17:39:18.462-07:00Looking for the magic bullet<div class="separator" style="clear: both; text-align: center;"><a href="https://docs.google.com/drawings/d/1g9do3S5xAuG3HJOD2H41Hk3ETTp87N35zfteQ43b3Ds/pub?w=480&h=360" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="240" src="https://docs.google.com/drawings/d/1g9do3S5xAuG3HJOD2H41Hk3ETTp87N35zfteQ43b3Ds/pub?w=480&h=360" width="320" /></a></div>Today I was asked for my opinion on ST Math. I have heard this type of question many times before. It goes something like this...<br /><br />"I have heard that ST Math improves student test scores. What is your opinion of XXXXX Elementary School asking the PTA to fund the annual subscription?"<br /><br />Here is my response today...<br />--------------------------------------<br /><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: x-small;">Hey there...</span> </blockquote><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;">I know ST Math (Ji Ji Math) pretty well. I've observed it in action and have been asked numerous times to give my opinion about it. In short, it costs a lot of money for minimal (if any) gains. Nearly all of the studies showing a benefit to students involved low-income students only. It is never made clear whether the students benefitted from ST Math specifically, or if students merely improved because ST Math provided "extra math time" and ANY extra math time would have created the same benefits. </blockquote><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;">It is pretty easy to find evidence on both sides of the ST Math question...<br /><b>Has no effect: </b><a href="https://www.researchgate.net/publication/260638069_A_Randomized_Trial_of_an_Elementary_School_Mathematics_Software_Intervention_Spatial-Temporal_ST_Math%C2%A0" target="_blank">https://www.researchgate.net/publication/260638069_A_Randomized_Trial_of_an_Elementary_School_Mathematics_Software_Intervention_Spatial-Temporal_ST_Math </a></blockquote><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><b>Has an effect:</b><a href="https://www.edsurge.com/news/arizona-students-catch-up-fast-with-st-math%C2%A0" target="_blank">https://www.edsurge.com/news/arizona-students-catch-up-fast-with-st-math </a></blockquote><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;">What worries me about schools that are considering ST Math is that there is a belief that ST Math will improve student results WITHOUT teachers having to change their instructional strategies. I've observed teachers in computer lab time using ST Math as a glorified babysitter. </blockquote><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;">The NUMBER 1 thing that improves mathematics achievement is improving the quality of the math instruction in the classroom. ST Math is low on the list. </blockquote><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;">My suggestion: Use the money to pay for PD that will improve the teaching that goes on in the classroom. Alternatively, the annual cost of ST Math could purchase 50 - 100 Chromebooks each year. </blockquote><blockquote class="tr_bq" style="color: #222222; font-family: arial, sans-serif; font-size: small;">Sorry dude. ST Math is not the magic bullet. What we need is just good teaching.</blockquote><div style="color: #222222; font-family: arial, sans-serif; font-size: small;">----------------------------------------------------</div><div style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div>When investigating ST Math, schools are attempting to outsource the instruction to a computer, while completely ignoring that the teacher's instructional strategies are far more important than ANY software. Unfortunately, all the money is spent purchasing the site license allowing no money left over to improve the quality of classroom instruction.<div><br /></div><div>Please...let's stop looking for a magic bullet. Instead, let's focus on using our mathematics instructional coaches effectively to improve classroom instruction.</div><div><br /></div><div>It is hard work, but much better than expending our time and energy looking for a magic bullet.</div><div><br /></div><div>.</div><div>.</div><div>.</div><div><div><br /></div><div><br /></div></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-76663349059575073042016-08-24T17:21:00.003-07:002017-07-01T09:58:37.018-07:00Pacing with Eureka Math (#EngageNY)<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-TZyM2x3VFPQ/V743bLAPemI/AAAAAAAAVbM/u0whogFkpgMunywvJtU7BVVKMWAd8ve0gCLcB/s1600/Screen%2BShot%2B2016-08-24%2Bat%2B5.09.41%2BPM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="265" src="https://1.bp.blogspot.com/-TZyM2x3VFPQ/V743bLAPemI/AAAAAAAAVbM/u0whogFkpgMunywvJtU7BVVKMWAd8ve0gCLcB/s400/Screen%2BShot%2B2016-08-24%2Bat%2B5.09.41%2BPM.png" width="400" /></a></div><div><br /></div>As the TK-5 mathematics instructional coach in my district, I am often asked about pacing the Eureka Math lessons. In fact, today I even received an email from a math coach in a neighboring district asking the same thing. Here is his question and my response...<br /><br /><b>The question</b><br /><div><i>Our teachers are one week in with implementing Eureka!!! Some are already very anxious around pacing of the lesson. Any advice around what to tell them when they are wanting to slow way down & take 2+ days to do one lesson? Teachers are worried about moving onto the next lesson without feeling like their students are really understanding the concepts. What something encouraging to tell them? Doing a new lesson every day is making teachers very nervous!</i></div><div><b><br /></b></div><div><b>My response</b></div><div>Pacing is a common first-year concern. Here are some quick tidbits...</div><div>1. Don't do ALL the fluency activities listed in the lesson. Only choose one, perhaps two of them. Perhaps, consider doing NONE of the fluency activities for that day.</div><div><br />2. Do not turn the Application problem into a teachable moment. It is a time for the students to practice using their brain. It is a time for the teacher to collect formative data about the progress of her students. It should NOT turn into a 20 minute mini-lesson on how to solve the problem correctly.<br /><div><br />3. Be efficient with the Concept Development. Aim for 20 minutes maximum. To be efficient, the teacher needs to have decided the night before exactly the sequence of example problems to do for the lesson. Don't do ALL the examples in class. </div><div><br /></div><div>4. Limit the time students do the "independent" practice (the Problem Sets) to ONLY 10 or 15 minutes! This means the Problem Set is a time-based event rather than a product-based event. Students are not expected to do ALL problems during the 10-15 minutes. </div><div><br /></div><div>5. The night before, the teacher should decide which problems in the Problem Set are "must do's", "could do's", and "extensions". While students are working on the Problem Set in class for 10-15 minutes, they should do the "Must Do" problems first. Then the "Could Do" problems. </div><div><br /></div><div>6. Save at least 5 or 10 minutes for the Student Debrief time. The teacher should pick one or two key debrief questions to ask the class. The teacher edition lists some questions the teacher might ask. Or the teacher can simply ask, "Would someone please explain their thinking for Question 4?"</div><div><br /></div><div>All of the above can easily be fit into a 45 minute time period.</div><div><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-R00aClP0Ehg/V745a4wwkZI/AAAAAAAAVbY/LBoAb7mzjOMxDBudSzHHwox7Mt0CIXafACEw/s1600/Screen%2BShot%2B2016-08-24%2Bat%2B5.18.20%2BPM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="120" src="https://2.bp.blogspot.com/-R00aClP0Ehg/V745a4wwkZI/AAAAAAAAVbY/LBoAb7mzjOMxDBudSzHHwox7Mt0CIXafACEw/s200/Screen%2BShot%2B2016-08-24%2Bat%2B5.18.20%2BPM.png" width="200" /></a></div><div><b>Now the question is "What do I do with my students who are struggling and need an extra day with this concept?"</b></div><div>The answer to this is often "Move to the next lesson anyway!"</div><div><br /></div><div>Often in Eureka Math, the lessons move very incrementally from one lesson to the next. If a student doesn't understand Lesson 4, move on to Lesson 5 because it is likely the student will suddenly have the Ah-ha moment in that lesson rather than in Lesson 4. This is a very different mentality than what teachers are familiar with.</div><div><br /></div><div>To help the struggling students even though the teacher has moved on to the next lesson, the teacher ought to consider how she can make the concept accessible to the students. Some ideas...</div><div><ol><li>hook up the student with a student partner</li><li>allow the students to use manipulatives to solve the problems rather than drawing the pictures</li><li>consider teaching the student a different method altogether (perhaps a method taught in a future module) even while the teacher also continues attempting to teach the student the original method</li></ol>I'm sure their are other ideas (I'm thinking UDL in particular), but this is enough to get the conversation going!</div><div><br /></div><div>.</div><div>.</div><div>.</div><div><br /></div></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-66849227246657673842016-08-24T17:21:00.001-07:002016-08-24T17:21:43.888-07:00Pacing with Eureka Math (#EngageNY)<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-TZyM2x3VFPQ/V743bLAPemI/AAAAAAAAVbM/u0whogFkpgMunywvJtU7BVVKMWAd8ve0gCLcB/s1600/Screen%2BShot%2B2016-08-24%2Bat%2B5.09.41%2BPM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="265" src="https://1.bp.blogspot.com/-TZyM2x3VFPQ/V743bLAPemI/AAAAAAAAVbM/u0whogFkpgMunywvJtU7BVVKMWAd8ve0gCLcB/s400/Screen%2BShot%2B2016-08-24%2Bat%2B5.09.41%2BPM.png" width="400" /></a></div><div><br /></div>As the TK-5 mathematics instructional coach in my district, I am often asked about pacing the Eureka Math lessons. In fact, today I even received an email from a math coach in a neighboring district asking the same thing. Here is his question and my response...<br /><br /><b>The question</b><br /><div><i>Our teachers are one week in with implementing Eureka!!! Some are already very anxious around pacing of the lesson. Any advice around what to tell them when they are wanting to slow way down & take 2+ days to do one lesson? Teachers are worried about moving onto the next lesson without feeling like their students are really understanding the concepts. What something encouraging to tell them? Doing a new lesson every day is making teachers very nervous!</i></div><div><b><br /></b></div><div><b>My response</b></div><div>Pacing is a common first-year concern. Here are some quick tidbits...</div><div>1. Don't do ALL the fluency activities listed in the lesson. Only choose one, perhaps two of them. Perhaps, consider doing NONE of the fluency activities for that day.</div><div><br /><div>2. Do not turn the Application problem into a teachable moment. It is a time for the students to practice using their brain. It is a time for the teacher to collect formative data about the progress of her students. It should NOT turn into a 20 minute mini-lesson on how to solve the problem correctly.</div><div>3. Be efficient with the Concept Development. Aim for 20 minutes maximum. To be efficient, the teacher needs to have decided the night before exactly the sequence of example problems to do for the lesson. Don't do ALL the examples in class. </div><div><br /></div><div>4. Limit the time students do the "independent" practice (the Problem Sets) to ONLY 10 or 15 minutes! This means the Problem Set is a time-based event rather than a product-based event. Students are not expected to do ALL problems during the 10-15 minutes. </div><div><br /></div><div>5. The night before, the teacher should decide which problems in the Problem Set are "must do's", "could do's", and "extensions". While students are working on the Problem Set in class for 10-15 minutes, they should do the "Must Do" problems first. Then the "Could Do" problems. </div><div><br /></div><div>6. Save at least 5 or 10 minutes for the Student Debrief time. The teacher should pick one or two key debrief questions to ask the class. The teacher edition lists some questions the teacher might ask. Or the teacher can simply ask, "Would someone please explain their thinking for Question 4?"</div><div><br /></div><div>All of the above can easily be fit into a 45 minute time period.</div><div><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-R00aClP0Ehg/V745a4wwkZI/AAAAAAAAVbY/LBoAb7mzjOMxDBudSzHHwox7Mt0CIXafACEw/s1600/Screen%2BShot%2B2016-08-24%2Bat%2B5.18.20%2BPM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="120" src="https://2.bp.blogspot.com/-R00aClP0Ehg/V745a4wwkZI/AAAAAAAAVbY/LBoAb7mzjOMxDBudSzHHwox7Mt0CIXafACEw/s200/Screen%2BShot%2B2016-08-24%2Bat%2B5.18.20%2BPM.png" width="200" /></a></div><div><b>Now the question is "What do I do with my students who are struggling and need an extra day with this concept?"</b></div><div>The answer to this is often "Move to the next lesson anyway!"</div><div><br /></div><div>Often in Eureka Math, the lessons move very incrementally from one lesson to the next. If a student doesn't understand Lesson 4, move on to Lesson 5 because it is likely the student will suddenly have the Ah-ha moment in that lesson rather than in Lesson 4. This is a very different mentality than what teachers are familiar with.</div><div><br /></div><div>To help the struggling students even though the teacher has moved on to the next lesson, the teacher ought to consider how she can make the concept accessible to the students. Some ideas...</div><div><ol><li>hook up the student with a student partner</li><li>allow the students to use manipulatives to solve the problems rather than drawing the pictures</li><li>consider teaching the student a different method altogether (perhaps a method taught in a future module) even while the teacher also continues attempting to teach the student the original method</li></ol>I'm sure their are other ideas (I'm thinking UDL in particular), but this is enough to get the conversation going!</div><div><br /></div><div>.</div><div>.</div><div>.</div><div><br /></div></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-85982723375831977062016-08-23T16:55:00.000-07:002016-08-23T17:47:59.389-07:00Three stages of counting<div id="contents"><div class="c3"><i>Today I had the pleasure of co-teaching a class of 1st graders. Being only the second week of the school year, I was amazed at how deftly the teacher peppered her math lesson with mini-lessons on the various routines and protocols of the classroom. This old former-math-teacher-turned-elementary-coach learned tons about how to run a 1st grade class. Humbling, truly humbling.</i></div><div class="c1"><i></i></div><div class="c3"><i><br></i><i>I was able to return the favor by sharing some math thoughts. Here is how our time progressed and my resulting mathematical thoughts...</i><br><br>The teacher began by posting two fish bowls on the board and used chips to represent goldfish. She put seven “fish” in one fishbowl and two in the other.</div><div class="c1"></div><div class="c3"><span style="-webkit-transform: rotate(0.00rad) translateZ(0px); border: 0.00px solid #000000; display: inline-block; height: 156.00px; margin: 0.00px 0.00px; overflow: hidden; transform: rotate(0.00rad) translateZ(0px); width: 423.00px;"><img alt="" src="https://docs.google.com/drawings/image?id=sMBaQSyWI1XkI0Zd2VgfImg&rev=39&h=156&w=423&ac=1" style="-webkit-transform: rotate(0.00rad) translateZ(0px); height: 156.00px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); width: 423.00px;" title=""></span></div><div class="c1"></div><div class="c3"><br>Teacher: “How many fish are in the left fishbowl?”</div><div class="c3">Class: “7!!”</div><div class="c3">T: “How many in the bowl on the right?”</div><div class="c3">C: “2!!”</div><div class="c3">T: “How can we use those two numbers to begin filling in this number bond?” (She posts a laminated number bond on the board.)</div><div class="c1"></div><div class="c3"><span style="-webkit-transform: rotate(0.00rad) translateZ(0px); border: 0.00px solid #000000; display: inline-block; height: 108.74px; margin: 0.00px 0.00px; overflow: hidden; transform: rotate(0.00rad) translateZ(0px); width: 143.50px;"><img alt="" src="https://lh4.googleusercontent.com/rcRfAcQ3NzEVq-qLVwF7sj2NcAr63MgA1Zmc0yEHu4kr6Dzne-ltRNVT6JMc7vhpTofIqfgXY3G8wcWDgSdU7hgrdGD1cEcy6TBLIRIxLlpRi_nj6A7m9RJepa148hFgFraTvFpi" style="-webkit-transform: rotate(0.00rad) translateZ(0px); height: 108.74px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); width: 143.50px;" title=""></span></div><div class="c1"></div><div class="c3">C: “Write a 7 in the top circle and a 2 in the bottom circle!” (The teacher does so.)</div><div class="c3">T: “What number should I put here?” (The teacher points at the big empty circle.)</div><div class="c3"><br></div><div class="c1"></div><div class="c3"><b>Here is where the cool thing happens…</b></div><div class="c3"><br></div><div class="c3">Some students began pointing at the chips one-by-one, clearly counting. Other students simply raised their hands.</div><div class="c1"></div><div class="c3"><br></div><div class="c3">T: “At the snap of my finger, say the answer.” (She snaps.)</div><div class="c3">C: “Niiiiiine!”</div><div class="c3">T: “How many fish are there in all?”</div><div class="c3">C: “Nine”</div><div class="c3">T: “7 plus 2 equals….” (She writes ‘7 + 2 =’ on the board.)</div><div class="c3">C: “Nine”</div><div class="c1"></div><div class="c3"><br><b>So what was the cool thing?</b></div><div class="c1"><b></b></div><div class="c3"><br>All the students got the right answer, and yet it was obvious that the students were in a variety of developmental stages of counting.</div><div class="c1"></div><div class="c3"><br>There are three stages of counting:</div><div class="c3">.....Stage 1: Count all</div><div class="c3">.....Stage 2: Count on</div><div class="c3">.....Stage 3: Make an easier problem (Use a strategy)</div><div class="c1"></div><div class="c3"><br><b>Stage 1: Count all</b></div><div class="c3">When given a group of 7 chips and a group of 2 chips and asked “How many are there?”, students in this stage count all 9 chips one-by-one. Students in this stage recognize the need for one-to-one correspondence as they count the chips. This is typical for students in Kindergarten.</div><div class="c0"><span style="-webkit-transform: rotate(0.00rad) translateZ(0px); border: 0.00px solid #000000; display: inline-block; height: 154.88px; margin: 0.00px 0.00px; overflow: hidden; transform: rotate(0.00rad) translateZ(0px); width: 327.50px;"><img alt="" src="https://lh6.googleusercontent.com/gAfhPlxSGC3RAEP61jMj3kbC1_gCNGqGs8lFH2tWufoYWIlXQeMlYoW3pzW2TbEvZYLENaYQcj9HVZkdM5Os3Uhw1h1eYn06W57UVksHA--4miUZ2lkoC-QFPyPxRSdq2aph3ycY" style="-webkit-transform: rotate(0.00rad) translateZ(0px); height: 154.88px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); width: 327.50px;" title=""></span></div><div class="c1"></div><div class="c3"><b><br></b><b>Stage 2: Count on</b></div><div class="c3">At this stage, students are able to see one group as an entity (recognizing the cardinality of the group) and count on from there, often touching each chip of the second group as they count. In 7+2, a student might say “Seeeeven, eight, nine” as he touches each of the two chips in the second bowl. Stage 2 is typically introduced in Grade 1 (although some Kinders may begin Stage 2) with the hope that all 1st graders will have this stage under their belt by the end of the year. </div><div class="c0"><span style="-webkit-transform: rotate(0.00rad) translateZ(0px); border: 0.00px solid #000000; display: inline-block; height: 163.53px; margin: 0.00px 0.00px; overflow: hidden; transform: rotate(0.00rad) translateZ(0px); width: 324.00px;"><img alt="" src="https://lh3.googleusercontent.com/C9SJlPjCQUgBY_KFpkZecbQwWy9khjZ4_Rk9qEs7bUL7m8YttD55-s09z7wEPNrIahDqW-N-zo7UzzoKVmfCDyrGLS_FORIw0SZERcVwJTy5FWJStpo9L1MwhqhSTUt2lbKZIPvq" style="-webkit-transform: rotate(0.00rad) translateZ(0px); height: 163.53px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); width: 324.00px;" title=""></span></div><div class="c1"></div><div class="c1"></div><div class="c3"><b><br></b><b>Stage 3: Make an easier problem (Use a strategy)</b></div><div class="c3">This stage is introduced in Grade 1 with the hopes that students will internalize this strategy later in Grade 1 or in Grade 2. This stage is easier to describe with a problem such as 8 + 5. A student in Stage 3 might take two from the five and give it to the eight, making 10. Then add 10 and the remaining 3 to get 13.</div><div class="c0"><span style="-webkit-transform: rotate(0.00rad) translateZ(0px); border: 0.00px solid #000000; display: inline-block; height: 174.23px; margin: 0.00px 0.00px; overflow: hidden; transform: rotate(0.00rad) translateZ(0px); width: 341.00px;"><img alt="" src="https://lh6.googleusercontent.com/-9fZxejukdN1GLjaC6hKPGWjywJ_w9M97FCfidjLMDKd8JIVi-J17oVdb4KXv50Uu5wcZ56767imXF4uutkV1WtOpcaoX8Mis7Yp2FeLYtcftwPYXpwRXPnoyO0xjeGDhh9K8mZt" style="-webkit-transform: rotate(0.00rad) translateZ(0px); height: 174.23px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); width: 341.00px;" title=""></span></div><div class="c3"><br>For a problem an addition problem within 10, students in Stage 3 might explain knowing 7+2=9 by saying something like “I just knew it in my head”.</div><div class="c0"><span style="-webkit-transform: rotate(0.00rad) translateZ(0px); border: 0.00px solid #000000; display: inline-block; height: 119.92px; margin: 0.00px 0.00px; overflow: hidden; transform: rotate(0.00rad) translateZ(0px); width: 344.50px;"><img alt="" src="https://lh4.googleusercontent.com/css9zhp4OBdSFlm6jKRKq9FChDsPvusqLWkWZCfUfz4F0K4k6Z6lwb6UQgkL1D-rYKk_REvLmAkdUJwO6bbrLzjzdWygydw99Eu49EtKLXZGCki-u5NA68HAEvYYPty70zA7vMAz" style="-webkit-transform: rotate(0.00rad) translateZ(0px); height: 119.92px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); width: 344.50px;" title=""></span></div><div class="c1"></div><div class="c3"><br><b>Why do we need to know the three stages of counting?</b></div><div class="c1"><b></b></div><div class="c3">It is not enough to see that a student has written “7 + 2 = 9” beneath the fish bowl on her paper. We teachers need to dig a bit deeper and determine with which stage did the student use to get that answer? A student who gets 100% on her paper is not considered fluent with basic facts if she uses “Stage 1 Count All” on every problem.</div><div class="c1"></div><div class="c3"><span class="c4"><br></span><span class="c4">Basic fact fluency requires the presence of flexibility, appropriate strategy use, efficiency, and accuracy. It is not enough to verify whether a student can correctly solve the problems in a timely fashion (ala “timed tests”...but that is a different blog post...ugh). Somehow, the teacher needs to also assess the flexibility and strategy use of each student. This is where number talks, small groups, and informal formative assessment comes in. Somehow for each student the teacher must identify the student’s current developmental stage (count all, count on, or make an easier problem) and then nudge that child to the next level up.</span></div><div class="c1"><span class="c4"></span></div><div class="c3"><span class="c4"><br></span><span class="c4">It was fascinating to watch the three stages in action during this single 1st grade lesson. It is humbling to me when trying to advise the teacher how to determine the stage of each child. I take comfort in the fact that if I was the teacher I wouldn’t worry about trying to assess the stage of EVERY student in a single day. Perhaps I’d use an anecdotal list to record the stages of the various students I happen to come across. Then specifically target the remaining students during centers time.</span></div><div class="c1"><span class="c4"></span></div><div class="c3"><br><b>My challenge to us all</b></div><div class="c3">When we wander around the room, looking over the shoulders of our kiddos at their answers, let’s try to go one step beyond merely checking if the answers are correct. Take a moment with one or two students per day to focus not only on WHAT is the student’s answer, but also HOW did the student arrive at that answer?</div><div class="c1"></div><div class="c3"><br>Oh yeah...while ensuring proper classroom control with the other 24 students. But THAT is for another blog post.<br><br><br><br></div><div class="c3"></div><div class="c1"></div></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-18949118808642073792016-08-10T11:50:00.000-07:002016-08-10T11:50:14.887-07:00Hattie's Interactive Visualization<br /><div class="separator" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><a href="http://visible-learning.org/nvd3/visualize/hattie-ranking-interactive-2009-2011-2015.html"><img border="0" height="145" src="https://1.bp.blogspot.com/-ifJ2ustkgLI/V6t21sQlhyI/AAAAAAAAVLA/-HzpCyg80twza8_EqDZ_Gpx2nHomsVxxwCLcB/s320/001.png" width="320" /></a></div><br /><div>We only have so much time in our day. How can we get the biggest bang for our buck with our limited time?</div><div><br /></div><div>Take a look at John Hattie's interactive visualization of influences on student achievement and their effect sizes. What is "effect size"? In layman's terms it is a unit of measure that allows us to measure the expected increase in achievement for a particular influence. The bigger the "effect size" the better. </div><div><br /></div><div>Here it is...</div><div><a href="http://visible-learning.org/nvd3/visualize/hattie-ranking-interactive-2009-2011-2015.html">http://visible-learning.org/nvd3/visualize/hattie-ranking-interactive-2009-2011-2015.html</a></div><div><br /></div><div>Of particular note...try to find homework. You will see that it is way, way down the list. Seems to me, all the energy we put into homework is for very little gain. Perhaps, we should refocus our energy on things that are demonstrably more beneficial to our students.</div><div><br /></div><div>Just sayin'.</div><div><br /></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-68130486826790062682016-08-10T11:07:00.000-07:002016-08-10T11:07:08.895-07:00"Self-Efficacy and Homework" or "The 'ifs' of Homework"<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-F23Z79Lgims/V6tstLCAZlI/AAAAAAAAVKw/4KT6S2Wr1KUY_vddcUu3YI9EJ2Xo7DxHwCLcB/s1600/pablo.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="160" src="https://3.bp.blogspot.com/-F23Z79Lgims/V6tstLCAZlI/AAAAAAAAVKw/4KT6S2Wr1KUY_vddcUu3YI9EJ2Xo7DxHwCLcB/s320/pablo.png" width="320" /></a></div>Today I was <a href="http://www.ernweb.com/educational-research-articles/how-much-homework-should-you-give-your-students-math-achievement/">reading this summary</a> of studies about the roles of homework and self-efficacy in closing the mathematics achievement gap. (<a href="http://www.ernweb.com/educational-research-articles/how-much-homework-should-you-give-your-students-math-achievement/">http://www.ernweb.com/educational-research-articles/how-much-homework-should-you-give-your-students-math-achievement/</a>)<br /><br />It seems to suggest two things...<br />1. Self-efficacy is essential in closing the achievement gap<br />2. Math homework is the way for students to develop self-efficacy<br /><br />Number 1 seems very reasonable. Indeed, I have come across <a href="https://www.google.com/#q=PISA+self-efficacy">many other studies</a> regarding self-efficacy and its role in math anxiety, achievement gap, and gender differences.<br /><br />Number 2, however, has me scratching my head. It is unclear to me why the authors of this study single out homework as the means for developing self-efficacy. Especially because it is entirely dependent upon the student having access to all necessary support resources at home in order to complete the math homework thereby developing the self-efficacy.<br /><br />It seems that many who support math homework do so with several "ifs" attached. For example, <a href="http://www.learningscientists.org/blog/2016/5/31-1">this blog post</a> ends with a series of such "ifs".<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-etKFql9gp8Y/V6toP0gqjlI/AAAAAAAAVKk/J7fsz_FpYQMszARAFe5dGrZhUMQw9BZTwCLcB/s1600/Screen%2BShot%2B2016-08-10%2Bat%2B9.47.47%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="392" src="https://4.bp.blogspot.com/-etKFql9gp8Y/V6toP0gqjlI/AAAAAAAAVKk/J7fsz_FpYQMszARAFe5dGrZhUMQw9BZTwCLcB/s640/Screen%2BShot%2B2016-08-10%2Bat%2B9.47.47%2BAM.png" width="640" /></a></div>Unless and until we work our the "ifs", issues such as math anxiety, ethnic/racial achievement gaps, and gender achievement gaps are likely to continue vexing our profession.<br /><br />While the adults are working out the "ifs" it seems we need to ensure we are doing no harm to the students. Reading for K-5 homework? No question...yes! No "ifs" there. Math for K-5 homework? Hold your horses...let's carefully work out the "ifs". In the meantime, <a href="https://talkingmathwithkids.com/2015/10/21/dont-help-with-homework-talk-about-math-instead/">definitely do this</a>!<br /><br /><br />Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-5541004395611486412016-05-25T19:20:00.001-07:002016-05-25T19:20:19.033-07:00Introducing EMBARC.Online<div style="text-align: center;"><span style="font-size: large;"><a href="http://embarc.online/">http://embarc.online</a></span></div><img height="160" src="https://lh3.googleusercontent.com/2OxZzlMTnjRxXtQaL0tBJEh75Xco3IJ9gzYDj-nob9m3U7OtRgppSZ0ZdC36eUIFKa-e0ok8utARxnZZK6aNL5ZjKaHtTpZXj8W2DsnAK83cH_ImJhOo2POz0HJfTzU4yTFM3z2x" width="320" /><br /><br /><b>I’d like to introduce you to EMBARC.Online.</b><br /><div><div style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="640" src="https://lh3.googleusercontent.com/r8QftD_aJyA_764i3B2l3EbeGhxrD5ZQt_Y6Pleh4lEnSWdA_FCgU6W6-EjlWAXQD0bls6iHH5IayItxQSglsCzlC9s-Hpi-Ahm00Oq-x6-AnTAXXOQdPQsz-7vpod0Sa8h_msVi" width="431" /></div><br />EMBARC stands for Eureka Math Bay Area Regional Consortium.<br /><br />Our vision is:<br /><ul><li>To build a <b>collaborative community</b> of Eureka Math users</li><li>To provide a common website to support <b>all</b> users of the Eureka Math curriculum</li></ul>Two years ago (2013-2014 school year), teachers in my district began using using bits and pieces of the EngageNY math modules. The following year nearly two-thirds of our teachers used EngageNY as their sole math curriculum while the Math Curriculum Adoption Committee spent the year deciding on a curriculum to adopt. As it turns out we adopted EngageNY, although we officially use the Eureka Math branding. (I could not be more proud of the teachers who specifically made the decision to adopt an ambitious curriculum that, while great for students, is challenging for adults.)<br /><br />During our time dabbling in using this wonderful curriculum, it became very clear to me - as the TK-5 Mathematics Instructional Coach - that our teachers were going to need a lot of support in order to fully understand and implement it. Thus began a steady stream of emails from me to my teacher community, sharing the “latest and greatest” web URLs, links, and resources.<br /><div><br /></div>I had every intention to be helpful. Indeed, I thought each new resource I shared was worthy of being used by the classroom teacher. Unfortunately, the teachers were drowning in the sea of “helpfulness” that was spewing from my email. The problem was that teachers had no time to read through the latest resource I shared, understand how it relates to the Eureka Math content being taught, and then assimilate it into the already lengthy lesson. After all, teachers were already complaining that the 60 minute Eureka Math lesson takes 90 minutes or more to complete...and now I was asking teachers to consider including this latest and greatest supplemental resource?<br /><br /><b>This is where EMBARC comes in.</b></div><div>Rather than sending teachers out to a variety of third-party locations (Illustrative Mathematics, Inside Mathematics, Zearn, Three-Act lessons, to name a few), we will curate the best of the web and organize it on EMBARC.online. Great supplemental resources will be placed right at the topic or lesson where they will be most useful. </div><div><br /></div><div>Are you a 5th grade teacher doing Module 5 Lesson 18 tomorrow? Navigate there and you will find great resources to choose from to supplement, augment, or totally re-write the lesson. The teacher can access the exact support she needs at the exact moment she needs it.<div style="clear: right; float: left; margin-bottom: 1em; margin-left: 1em;"><br /><br /><img height="320" src="https://lh3.googleusercontent.com/h3WR_BIAwtQqI6ibWzqFcJca5KSfLx-TNrAJg1iiQsQeiRXhyaYNFBFC92Zb2veHaSypC-R0wVl9JocmOsgLURzepI9B86GjSCkSx0RNI-EiUnz1bKuR4ntobTWCYTlWDIechK12" width="266" /></div><div><br /></div>Curating outside content into the curriculum is the first way that EMBARC distinguishes itself from other EngageNY/Eureka Math website. Nearly all EngageNY/Eureka Math websites have the core materials as PDFs ready for download and that’s about it. For additional resources, teachers are usually sent to external links to fend for themselves. EMBARC curates to make things easier on the teacher. We bring the resources in for the teacher, rather than sending the teacher outside to other sites.<br /><br /><b>A collaborative community</b><br />A second, more profound distinction is the collaborative community on EMBARC. Every module has a “Faculty Lounge”, in which our users can share ideas: new resources, shared Pinterest link, ideas for pacing.<br /><br /><img height="175" src="https://lh6.googleusercontent.com/3dloyEyjO2JRKFZEF24QItv-vA4vHXr1RSMWMujP1qHiXUERpFBADfGGFNgfRZhG-t6A6TAaRTWZndNJsa7X-7Kqg2ACmOTM_O041FI1WkJWNJEq7e1T3S9lsqFb1DOBr0hndpr5" width="512" /><br /><br /><br />Our EMBARC editors will find the best ideas shared in the Faculty Lounge and integrate them through the rest of the module. Teachers learn so much around the lunch table! We re-create that experience in the Faculty Lounges on EMBARC.<br /><br /><b>Now what?</b><a href="http://embarc.online/login/signup.php">Join the community!</a> Take part in a community of Eureka Math users who support each other, share ideas, and collaborate.<br /><br /><a href="http://embarc.online/">EMBARC</a> is entirely free to use. No account is necessary. However, you will need to create a free account in order to contribute to the discussion in the faculty lounges.<br /><br /><div>The more people who join in on the conversation, the more we support each other, the better we will be for our students.<br /><br /><a href="http://embarc.online/" target="_blank"><img height="66" src="https://lh5.googleusercontent.com/FelKRGcC9XB1Lrlk7TSAcaFUQ_0fpElOqKz6hDGMWZHLZS4_sgzrsls3TcN2qBLLr6KltJjg2w6yXHQOpUQOLrtxwbTWJdSjOp24TGdiWrNNV8jUdg_tDG-1J7exS9dBxcI2aQpa" width="576" /></a></div><div>.</div><div>.</div><div>.</div></div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-79061574758068099072016-05-10T23:18:00.000-07:002016-05-10T23:18:08.594-07:00Is a parallelogram also a trapezoid? A famous bard once said, “A trapezoid by any other name would still be a trapezium”. <br /><br />Okay...totally not true. But it brings to mind the question I am often asked, “What is the definition of a trapezoid?” In fact, I was asked this question today. So here is my answer…<br /><br />For mathematics, being a subject that is supposedly the “universal language”, this question opens a huge can of worms and has a surprisingly involved answer.<br /><br />There are three – yes three – different ways one can define a trapezoid. Let’s get started.<br /><br />If a person walks up to you and says, “Let’s discuss trapezoids”, the first things you should do is listen his accent. Is it American? Is it Canadian? Or some other English-speaking accent? This matters.<br /><br />For the words trapezoid and trapezium, America and Canada defines them one way, but in other English speaking countries these same two words have their meanings switched.<br /><br />In America and Canada...<br /><div><table><tbody><tr><td>trapezium</td> <td>trapezoid</td></tr><tr><td><img src="https://docs.google.com/drawings/u/0/d/swjph_mbcqHUeM8sEZnKylg/image?w=175&h=109&rev=3&ac=1" /> <br /><br /><br /></td> <td><img src="https://docs.google.com/drawings/u/0/d/sodUjKNFxoIKChxPxbaH8lg/image?w=218&h=84&rev=22&ac=1" /></td></tr></tbody></table>In other English speaking countries...<br /><br /><table><tbody><tr><td>trapezium</td> <td>trapezoid</td></tr><tr><td><img src="https://docs.google.com/drawings/u/0/d/sAkevvJyCMnHIyMw0cUOkIg/image?w=218&h=84&rev=1&ac=1" /> <br /><br /><br /></td> <td><img src="https://docs.google.com/drawings/u/0/d/sOZy9sVh4-wAY4dAm6jbwYg/image?w=175&h=109&rev=1&ac=1" /></td></tr></tbody></table><br />In America a trapezium is a quadrilateral that has no parallel sides. Sometimes this is called an irregular quadrilateral.<br /><br />So now that we have define a trapezoid to be the figure that is not a trapezium. There is still the matter of the two definitions of trapezoid in America.<br /><br />Let’s start with this figure…<br /><br /><img src="https://docs.google.com/drawings/u/0/d/sK7uA945T5XAa7he1ufmBFg/image?w=218&h=84&rev=1&ac=1" /><br /><br />Most people would immediately recognize it as a trapezoid. There are two ways we can classify as trapezoid: the inclusive definition and the exclusive definition.<br /><br />T(I): a figure with at least one pair of parallel sides<br />T(E): a figure with exactly one pair of parallel sides<br /><br />Both definitions are legitimate, but they each lead to other differences in classifications.<br /><br />For example, a parallelogram is just a parallelogram in T(E), but a parallelogram is also a trapezoid in T(I).<br /><img src="https://docs.google.com/drawings/u/0/d/sa-kfn6G57FQObILIm9XVng/image?w=330&h=106&rev=72&ac=1" /><br /><br />In T(I), even a square is considered a trapezoid!<br /><br /><br /><b>Why can’t we all just get along?</b><br />We don’t need to argue over which definition is correct. They both are. So, this means when we speak about trapezoids, we must preface it with an agreement of which definition we are using...at least for that instance.<br /><br />T(E) seems to have its origins in the 1500’s prior to the advent of calculus. When calculus came along, we began using trapezoids to estimate the area under curves.<br /><br /><br /><a href="https://commons.wikimedia.org/wiki/File:Trapezoidal_rule_illustration.png#/media/File:Trapezoidal_rule_illustration.png"><img height="152" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Trapezoidal_rule_illustration.png/1200px-Trapezoidal_rule_illustration.png" width="200" /></a><br />Public Domain, https://commons.wikimedia.org/w/index.php?curid=647823<br /><br /><a href="https://en.wikipedia.org/wiki/File:Trapezium.gif#/media/File:Trapezium.gif"><img src="https://upload.wikimedia.org/wikipedia/en/a/ab/Trapezium.gif" /></a><br /><a href="http://creativecommons.org/licenses/by-sa/3.0/">CC BY-SA 3.0</a>, https://en.wikipedia.org/w/index.php?curid=44244531<br /><br />As the animation shows, some of the trapezoid slices begin to look suspiciously like rectangles. Aha!!! This is when T(I) got invented.<br /><br /><br /><b>Common Core Standards</b><br />In <a href="http://www.corestandards.org/Math/Content/5/G/">5th grade the standards</a> are non-committal on the trapezoid issue.<br /><br /><img height="133" src="https://lh5.googleusercontent.com/x6af6_tKpOzp1x2ncZzym5daWAPcbfjBPYwZRL5i5SU5shrzZbXq6I_k36svsND3GfL3U6oV8kkQMjvI6X8QaEitooikVSKmzOkfT8lUxyJMJjqxWE6ozH_ajKriJTlf2kiESUKf" width="400" /><br /><br /><br />The <a href="http://www.corestandards.org/Math/Content/3/G/">3rd grade standards</a> also sidestep the issue.<br /><br /><img height="116" src="https://lh6.googleusercontent.com/FPAyVCweH1YCut3k9gcKQcr6c4eqp6bH60JuuLcFE2fIUB77tJXM_c4CdiMK5hMc_d11Qmk9tHS6E2_jTFxlPnu7M3i1QSR6QfBp3NncHNIE-gOUvtUpfDmoK7HXjdlVZcVExbX4" width="400" /><br /><br />But the <a href="http://math.arizona.edu/~ime/progressions/">Progressions Documents for the Common Core Math Standards</a> make it clear that mathematicians prefer we use T(I).<br /><br /><img src="https://lh4.googleusercontent.com/FNqsYJHHzeLYEfsOWbRrSswbkKpFlOzaqvXVOnQ_OXEbVrez6wE6MZ9q7xwCOzqFr3XoZrtaqzYXhU_Gc5t7MCB6Xw6uytl6WltKq7sSmCJfJicVwcK70ET1nSsXRYc3b7nT8tsB" /><br /><br /><br />Since a key component of the Common Core Standards is that students will be <a href="http://www.corestandards.org/about-the-standards/">college and career ready</a>, it seems the best trapezoid definition to use is the one that leads to calculus...T(I).<br /><br />These are all trapezoids…<br /><br /><img src="https://docs.google.com/drawings/u/0/d/sjajTBPs-f2nwCBgMi-8pwg/image?w=176&h=68&rev=1&ac=1" /> <img src="https://docs.google.com/drawings/u/0/d/sDqTmAybIKb0scIppJ4dRRQ/image?w=229&h=73&rev=1&ac=1" /> <img src="https://docs.google.com/drawings/u/0/d/sYmdXj4JxyRpXzFYyxV0HvA/image?w=78&h=78&rev=3&ac=1" /><br /><br /><br /><div style="text-align: center;"><b><i><span style="color: #6aa84f;">A trapezoid is a quadrilateral with at least one pair of parallel sides.</span></i></b></div><div style="text-align: center;"><br /></div>.<br />.<br />.</div>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-48309430198534567122016-05-02T17:46:00.002-07:002016-05-02T17:46:24.748-07:00Eureka Math Grade 5 Module 6 #engageny #eurekamath<div class="separator" style="clear: both; text-align: left;"><a href="https://1.bp.blogspot.com/-QWvtjFlHXUA/Vvwgkng01rI/AAAAAAAAQ-Y/GUAr8agdDrwzO8RDT3iTghDFQmY1HzdFwCKgB/s1600/Grade5Module_06.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://1.bp.blogspot.com/-QWvtjFlHXUA/Vvwgkng01rI/AAAAAAAAQ-Y/GUAr8agdDrwzO8RDT3iTghDFQmY1HzdFwCKgB/s320/Grade5Module_06.png" width="320" /></a></div><br /><iframe allowfullscreen="" frameborder="0" height="344" src="https://www.youtube.com/embed/videoseries?list=PLvolZqLMhJmlAKrlymK7nFy1YFDUOlWr1" width="425"></iframe><br /><br />For the rest of our Eureka Math resources, visit <a href="http://bit.ly/eurekapusd">http://bit.ly/eurekapusd</a><br /><br />.<br /><br />.<br /><br />.Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0tag:blogger.com,1999:blog-322105099655560837.post-465811992345367352016-05-02T16:05:00.001-07:002016-08-10T08:57:01.415-07:00What research says about the value of homework: Research review<br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="https://c1.staticflickr.com/6/5786/20786659744_61b579b646_b.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="133" src="https://c1.staticflickr.com/6/5786/20786659744_61b579b646_b.jpg" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span id="docs-internal-guid-b8583908-73ba-2610-4c93-d5b5ae778b24"></span><br /><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span id="docs-internal-guid-b8583908-73ba-2610-4c93-d5b5ae778b24"><span style="font-family: "arial"; font-size: 13.3333px; vertical-align: baseline; white-space: pre-wrap;"> Retrieved from</span><a href="https://c1.staticflickr.com/6/5786/20786659744_61b579b646_b.jpg" style="text-decoration: none;"> Flickr with permission</a></span></div><span id="docs-internal-guid-b8583908-73ba-2610-4c93-d5b5ae778b24"></span></td></tr></tbody></table><div style="text-align: center;"><br /></div><span style="font-size: medium;">Given that homework is such an engrained aspect of the K-12 culture, you'd think there must be clear evidence that the homework being assigned is beneficial. You'd be wrong. Researchers are nowhere near consensus on the benefits of homework. In general, there appear to be something research agrees on...</span><br /><span style="font-size: medium;">Homework in elementary school has zero effect.</span><br /><span style="font-size: medium;"><br /></span><span style="font-size: medium;">To read more about the confusing state of what research says about homework, </span>go <a href="http://ift.tt/1SVrbHr">HERE.</a>Duane Habeckerhttps://plus.google.com/112411498608350686282noreply@blogger.com0