Wednesday, August 24, 2016

Pacing with Eureka Math (#EngageNY)


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...

The question
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!

My response
Pacing is a common first-year concern. Here are some quick tidbits...
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.

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.

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. 

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. 

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. 

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?"

All of the above can easily be fit into a 45 minute time period.

Now the question is "What do I do with my students who are struggling and need an extra day with this concept?"
The answer to this is often "Move to the next lesson anyway!"

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.

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...
  1. hook up the student with a student partner
  2. allow the students to use manipulatives to solve the problems rather than drawing the pictures
  3. 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
I'm sure their are other ideas (I'm thinking UDL in particular), but this is enough to get the conversation going!

.
.
.

Pacing with Eureka Math (#EngageNY)


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...

The question
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!

My response
Pacing is a common first-year concern. Here are some quick tidbits...
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.

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.
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. 

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. 

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. 

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?"

All of the above can easily be fit into a 45 minute time period.

Now the question is "What do I do with my students who are struggling and need an extra day with this concept?"
The answer to this is often "Move to the next lesson anyway!"

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.

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...
  1. hook up the student with a student partner
  2. allow the students to use manipulatives to solve the problems rather than drawing the pictures
  3. 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
I'm sure their are other ideas (I'm thinking UDL in particular), but this is enough to get the conversation going!

.
.
.

Tuesday, August 23, 2016

Three stages of counting

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 was able to return the favor by sharing some math thoughts. Here is how our time progressed and my resulting mathematical thoughts...

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.

Teacher: “How many fish are in the left fishbowl?”
Class: “7!!”
T: “How many in the bowl on the right?”
C: “2!!”
T: “How can we use those two numbers to begin filling in this number bond?” (She posts a laminated number bond on the board.)
C: “Write a 7 in the top circle and a 2 in the bottom circle!” (The teacher does so.)
T: “What number should I put here?” (The teacher points at the big empty circle.)

Here is where the cool thing happens…

Some students began pointing at the chips one-by-one, clearly counting. Other students simply raised their hands.

T: “At the snap of my finger, say the answer.” (She snaps.)
C: “Niiiiiine!”
T: “How many fish are there in all?”
C: “Nine”
T: “7 plus 2 equals….” (She writes ‘7 + 2 =’ on the board.)
C: “Nine”

So what was the cool thing?

All the students got the right answer, and yet it was obvious that the students were in a variety of developmental stages of counting.

There are three stages of counting:
.....Stage 1: Count all
.....Stage 2: Count on
.....Stage 3: Make an easier problem (Use a strategy)

Stage 1: Count all
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.

Stage 2: Count on
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.

Stage 3: Make an easier problem (Use a strategy)
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.

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”.

Why do we need to know the three stages of counting?
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.

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.

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.

My challenge to us all
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?

Oh yeah...while ensuring proper classroom control with the other 24 students. But THAT is for another blog post.



Wednesday, August 10, 2016

Hattie's Interactive Visualization



We only have so much time in our day. How can we get the biggest bang for our buck with our limited time?

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. 

Here it is...

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.

Just sayin'.

"Self-Efficacy and Homework" or "The 'ifs' of Homework"

Today I was reading this summary of studies about the roles of homework and self-efficacy in closing the mathematics achievement gap. (http://www.ernweb.com/educational-research-articles/how-much-homework-should-you-give-your-students-math-achievement/)

It seems to suggest two things...
1. Self-efficacy is essential in closing the achievement gap
2. Math homework is the way for students to develop self-efficacy

Number 1 seems very reasonable. Indeed, I have come across many other studies regarding self-efficacy and its role in math anxiety, achievement gap, and gender differences.

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.

It seems that many who support math homework do so with several "ifs" attached. For example, this blog post ends with a series of such "ifs".
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.

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, definitely do this!