Tuesday, February 23, 2016

Because Students Might Learn

About a hundred years ago (at least it feels that way) I was a 7th grader in Mr. Munson's math class. Each night's homework was always posted on the chalkboard. It would look something like...
Whatever the page, we ALWAYS did the even numbered problems. Particularly vexing was that we seventh graders knew the answers to the odd problems were in the back of the book. "Is today the day he going to assign the odds?", we would ask each other as we waited outside for Mr Munson to let us in to class. Each day, however, it was the evens. ALWAYS the evens.

Finally one day I worked up the nerve to ask Mr. Munson, "Why is it always the evens? Don't you know the odds are in the back of the book?"

"Yep," he said, "that's why I assign the evens. I don't want give you the answers. You have to work for it." "But how do we know if we are doing it right?", I replied. "The odds would help us do it right."

"I assign the evens", he said, and it was clear the conversation was over.

I was 12 and knew that having the answers in the back of the book was an invaluable tool for learning. The answers were the feedback I needed in order to know I was on the right track.

This sort of stuff still goes on. For some reason teachers intentionally prevent students from accessing useful learning tools:
  • Our Eureka Math curriculum did not initially come with answers. So, I created solution manuals for many of the modules in Grades 3 through 5. Teachers, while grateful to have the solution manual, were not happy that I posted the answers on the district web site. "Students might look at the answers while doing their homework," the teachers said. "Right," I said, "and looking at the answers might help a struggling student learn the math."
  • I have created tutorial videos for every lesson in Eureka Math. Initially the purpose was to help teachers understand the math they were supposed to teach, but students started watching the videos too. I made the videos on selected Homework problems, so that parents could also watch the videos in an effort to understand the math and help their child. My goal: no more homework fights. Teachers, however, suggested that students might copy from the videos. "You mean students might receive help on the exact problems they are struggling with?", I answered with mock concern.
  • During a districtwide assessment meeting a teacher voiced her concern that if students were allowed to retake tests, students would continually retake the test until they mastered the concept.
I've got an idea: Let's give students MORE tools to assist with their learning...not less!

Answer keys, tutorial videos, and test re-takes might be just the thing that students need to help them get over the hump and learn whatever concept you are teaching. 

Why should we do this? Because students might learn.

Are there other things teachers do to PREVENT students from learning? Chime in below...

Tuesday, February 16, 2016

Draw a Mathematician

One day many years ago I was teaching 6th grade math at a middle school, when I was having an incredibly hard time getting my students to think like mathematicians. It seemed that no amount of cajoling, encouraging, and cheerleading on my part could convince my students to get out of their passive (passive-aggressive?) blob-like frame-of-mind. It was clear to me that I was dealing with a much greater problem than the mere math problem at hand.

In one of those moments that are best characterized as "half desperation and half inspiration" I asked my students to put down their pencil and take out  a piece of scratch paper. I told my students that in a moment they would be sketching a quick picture after they listened to me describe the scenario.

"Imagine," I said, "that I have invited a mathematician to speak to our class."

I continued. "That mathematician is on the other side of our door and is about to enter this room. The door opens. In comes the mathematician who then stands at the front of the room."

I scanned the room of 6th graders in wrapt attention. Some were even closing their eyes to truly see the mathematician. "In your minds eye," I continued "what is the mathematician wearing? What does the mathematician look like? Sound like?"

I then told my students to take a few moments to sketch the mathematician that they imagined in their mind. "NO peeking at your neighbor's drawing!" I admonished. Of course, students asked if they would be graded on the quality of their drawing (ugh...grades...that is another blog post), which of course, I said they would not.

Students quietly drew for several minutes, some even getting the colored pencils and marking pens from the back of the room. I wandered around the room looking at the drawings. Here is what I saw:

Of the 30 students in the class, 29 drew a picture of a male. Only one student - a girl - drew a female mathematician. Now here is the kicker...every drawing portrayed the mathematician in a negative light. Broken glasses. Messy hair. Horns and a devil's tail. Fangs. Every student included some sort of indicator that being a mathematician was to be AVOIDED not admired.

No wonder I was having a hard time getting my students to act like mathematicians! A mathematician - to my students - was a horrible, horrible thing.

I immediately started a campaign to rectify this. I tore down the numbers hanging from the ceilings to indicate table groups and replaced them with names of mathematicians. No more Table 1 or Table 2. Now it was the Euclid Table. The Germain Table. The Ramanujan Table. Moreover, I called the students by their table name. "Would the Brahmaguptas and the Eulers come to the front of the room for small-group?" Students began calling themselves by their "math name".

Scattered throughout the year, I would read from Mathematical Scandals, by Theoni Pappas, showing my students that some mathematicians have pretty awesome (almost rock star-like) lives.
It was always pretty easy to connect something we were currently learning with a short and fascinating tale of some mathematician.

I never did a follow-up experiment with my students to measure growth in this area. What would the pictures of the imaginary mathematician look like today? I'm not sure...

I have a bit of insight as to what students might draw. They might draw me!

I am now a mathematics instructional coach for TK-5 in a school district that recently adopted Eureka Math. To assist with the transition to this wonderful curriculum I began making videos for every single lesson, so that teachers could first learn the mathematics from me before they have to teach it to their students the next day. Then parents began watching the videos at home to help their kids with homework. Inevitably, students see my videos as well.

Daily I get comments from students around the nation like...

When I am visiting classrooms at an elementary school, students bring up their math booklets for me to autograph. 

Recently, teachers have begun scheduling Google Hangouts with me to meet their students.

Other adults are now sending in questions...

The cool thing about all this is not how it makes me feel. (Although, it does indeed make me very, very pleased.) The best thing is that I am seen as a MATHEMATICIAN. Male, yes. But no broken glasses. No messy hair. No horns and devil's tail.

It seems that my proudest contribution to this instructional coach thing is that - in my own little way - I have not only gotten teachers to grow, but students too!

What things do YOU do to make being a mathematician something to aspire to?

Tuesday, February 2, 2016

EngageNY Grade 3 Module 5 #eurekamath #engageny

For the rest of our resources for Eureka Math (EngageNY), visit http://bit.ly/eurekapusd




Eureka Math Grade 4 Module 5 #eurekamath #engageny

For the rest of our Eureka Math (EngageNY) resources, visit http://bit.ly/eurekapusd




I’ve Got the Data, Now What Do I Do with It? — Eureka Math — Medium

At a recent professional development event with Julia Payne-Lewis, an assessment specialist at Mind the Gaps, Eureka Math writers looked at research that reveals the powerful impact on student achievement of teachers using formative assessment to provide immediate feedback.

Read more via Pocket

Number Talks for ELL Students #numbertalks #numbertalk

I have long viewed Number Talks as the gateway drug to Common Core. Teachers who regularly use Number Talks in their classroom are inherently embracing some of the Standards for Mathematical Practice. In particular,

SMP1: Make sense of problems and persevere in solving them.

SMP2: Reason abstractly and quantitatively.

SMP3: Construct viable arguments and critique the reasoning of others.

Not sure what a Number Talk is? Go here and then come back.

A big question my teachers often ask is "What do I do with my ELLs during Number Talks"?

The answer is do Number Talks especially if you have ELLs in your classroom.  To support language development and content understanding we must create as many opportunities as possible for students to participate in whole-group and peer discussions in the classroom. Language learners need lots of opportunities to rehearse new academic language, especially as it is applied to relevant and authentic contexts.

As a result, teachers need to be very deliberate about creating safe opportunities for students to talk mathematically, engaging all students - especially our language learners.

Here is an example of a 1st grade teacher using Dots to get students to think about counting and numeracy. Pay attention to the open-ended mathematical thinking going on. Also notice that this kind of teaching requires the teacher to think on her feet. I assure you, however, after you've done a bunch of number talks, it becomes second nature for the teacher. 

Number Talks create a safe space for students to think about open-ended problems. Students learn that math is more than just solving one problem and moving on to the next problem; a key aspect of math is solving one problem in many ways.

Clearly, it may sometimes be tricky to get students actively engaged in the discussion - especially with ELL students. This is where the art of teaching meets the science of teaching. GLAD strategies are invaluable tools for supporting all students, allowing them to participate in academic conversations. Sentence frames should be a huge part of an elementary teacher's repertoire.

Without a doubt Number Talks benefit all students. Once firmly a part of a classroom's culture, I've seen entire classes of students who previously hated math suddenly love it. The bonus is doubled when we have ELL students in our classroom too!

Let me know if I'm off base on this...chime in below...


Monday, February 1, 2016

Math + Politics = Procrastination

Clearly I was not interested in writing the dreaded benchmark that was due today because when I saw Justin's tweet, I immediately jumped at the opportunity to get distracted.

This got me to thinking...how can we insert humor into our math classroom? Does a student's ability to use mathematical humor indicate some level of mathematical understanding?

Can anyone think of examples when a student's ability to use math humor clearly indicated math understanding?

Share below...