Our Journey Toward Equity in Mathematics (Part 1)

After falling in love with teaching mathematics in the classroom, I knew that I wanted to eventually end up in a learning support role for mathematics instruction.   Shortly after attending a Math Add+Vantage training offered by our district Title 1 department, I accepted a position as a K-5 Numeracy Coach.  I was trained shortly after as a Math Recovery Intervention Specialist.

I spent six years working with teachers on intervention and instruction.  The schools I worked in had some of the highest (over 85%) free and reduced lunch rates in our district.  Students came to us with varied educational backgrounds, many with very few experiences in numeracy.   In Title 1 Math, we utilized an instructional configuration for Math Workshop that the team had created based on the Comprehensive Literacy Model.  I worked with teachers to get math workshop and guided math set up in their rooms for those six years.  We looked at data, we visited other classrooms, we pre-assessed and re-assessed.  Our students were showing growth, but they weren’t making huge gains in proficiency.  The question was, why?

I learned many lessons in my years as a coach, but probably the one that has influenced my philosophy on education the most is that it is possible to intervene too much; and we were doing it.  I had set my expectations for students too low and was not exposing them to tasks that allowed them enough time and space for productive struggle.  We were so concerned with meeting students “where they are” that we had completely shifted instruction to intervention and removed the rigor.  I’d like to say that this realization came overnight, but the truth is it came after years of reading, learning, teaching, reflecting, and examining my practice.  To be honest, I’m still on the journey.

Two years ago, I accepted the curriculum coordinator position in our district for K-12 Mathematics.  The position had been re-imagined and was posted as Coordinator of 21st Century Numeracy.  When I accepted my current position, I was charged immediately with putting in place a math workshop model for all of our elementary buildings.  I was excited about this because I knew it would help teachers be more purposeful about instruction and this created opportunities to open dialogue about student understandings and next steps for instruction.

I told myself that we were doing workshop right because we had flexible groups that changed regularly.  But the truth was, in practice, that wasn’t the case in every classroom and even with flexible grouping, we were still tracking students into ability groups that stayed fairly stagnant.  Even though our practices were perhaps the best case scenario for math workshop, we were missing the boat on many other aspects of high quality instruction.

I also struggled with where and when to use high quality tasks such as 3 Act math tasks.  Our current structure did not allow for those opportunities.

It was really a perfect storm that led me to my current understandings and beliefs.

Jo Boaler‘s book, Mathematical Mindsets, spoke to my heart.  The findings that she proposed based on brain research that a) everyone can learn math at high levels, b) mistakes are really important in the learning process, and c) we must value depth over speed, made me look at our practices through a new lens.

It was Dan Meyer‘s Ted Talk that introduced me to 3 Act Math years and years ago that helped me develop my belief in problem based learning (and become obsessed with creating 3 Act math tasks for elementary).  I’ve had the opportunity to attend a few of Dan’s sessions at conferences since then and his words stuck with me, “Be Less Helpful.” 

I couldn’t reconcile those words against some of our instructional practices.  Everything we had designed to support students was about being more helpful – which had the effect of making them helpless.  We noticed that when students faced something difficult, they would immediately ask for help instead of persevering.  (For my thoughts on praise and learned helplessness, check out my prior blog post, How Do I Change Math Class Tomorrow?)

It was Robert Kaplinsky‘s Open Middle problems that provided the perfect model of how a task with multiple entry points could allow all students to engage in high quality math tasks.

It was Christopher Danielson‘s books, Which One Doesn’t Belong and How Many?, that tugged at the importance of sense making.

It was Sherry Parrish‘s book, Number Talks, that allowed me to look at fact fluency and number sense in a whole new light.

It was Brian Bushart‘s Numberless Word Problems, Steve Wyborney‘s Estimation Clipboard, Fawn Nguyen‘s Visual Patterns…the list goes on and on.

It was Graham Fletcher‘s link between 3 Act Math and the 5 Practices that had me looking at the power of combining high quality tasks and intentional teacher moves.

In 2017, at the NCSM National Convention, I was given a copy of Jennifer Lempp‘s Math Structuresnew book, Math Workshop.  In her book, Jennifer proposed a mix of guided math days and what she calls task and share days.  Task and share days were essentially days in which students work in heterogeneous groups to solve problems and share their solutions with the class. 

It was after reading her book that I realized it was time to modify our instructional model.  The following year we introduced two instructional models: Math Workshop days and Problem Solving days.  

That was our first step in a journey toward equitable teaching practices.

I truly believe that the lack of quality tasks (with multiple entry points) is the reason we have struggled with mathematics instruction for so long and why we have not been able to shift our pedagogy from teacher-centered to student-centered instruction.  As the list above clearly shows, that time is over.  In my future blog posts, I will share other open source resources for high quality curriculum that puts students in the drivers seat of enduring understanding.

3 Act: Stick Up Robot

I happened to be at Staples and I glanced down the Post-it aisle and noticed that not only was there a giant pad of Post-it notes but now they had come out with an even bigger pack of Post-it notes!  I bought them not knowing exactly how I would use them.  I remembered some other 3 Act tasks I had seen using Post-its and an article I read last year in an NCTM journal about using Post-its for area and perimeter. I thought about how I could use them in a task for area in a way that makes it a little more engaging for kids and that’s how Stick Up Robot came about.

3.MD.C.5.B

Google Slide Deck

Act 1

How many tiles would it take to cover the whole robot?

Estimate.  Write a too low and a too high estimate.

Act 2

Yellow Post-it

Pink Post-it

Teal Post-it

Tiled Teal Post-it

Robot Blackline (can print as a scaffold for organizing work)

Act 3

Robot Total

3 Act: Gotta Count ‘Em All

Recently I’ve been reading the book Counting Collections and I got really inspired to create some three act tasks that played on the counting collections structure. I particularly liked the sections about recording student work and I thought this would be a really great visual for students to take back to their work with counting collections to think about different ways that they could record their work but also different ways that they could group and organize numbers when counting large collections.

My son is a huge Pokemon fan and had this great little assortment of Pokemon.

This task can be used for assessing multiple standards and practices, but I settled on 2.NBT.B.7.

Google Slide Deck

Act 1

 

What do you notice?  What do you wonder?

How many Pokemon altogether?

Make an estimate that is too low, one that is too high and one that is about right.

Act 2

There were 4 cups of 25 Pokemon and 20 more.

Act 3

 

Act 3 Final Count

3 Act: Be There or Be…

This three act task is based on the Jo Boaler task that she shows in her Ted Talk video where the different color tiles are falling and people see the pattern emerge in different ways,  Although this shows only one way of the colors being added, it’s a great visual representation of how a pattern grows and and looking at perfect squares I just thought this was such a great task for students to grapple with in this way.   Although this task is great for many standards, I have chosen to link it to numeric patterns 4.OA.C.5.

Google Slide Deck

Act 1

What did you notice? What do you wonder?

Focus Question: What will the 5th shape look like? or How many tiles will be in the 5th shape?

Act 2

Act 2

Act 3

3 Act: Star Pattern

We play a game in stations to practice skip counting called “Cross the Creek” or “Cross the Galaxy.”  Basically we rename it based on the shape of the foam tiles.  The way the game works is that you write multiples of a number or a counting pattern on one side of craft foam pieces.  You then lay it out face up so that students can practice seeing and counting.  Students take turns walking across the numbers and saying them as they walk.  After they cross, they can choose one number to turn over and then the next person goes.  It’s a really great kinesthetic way to get kids to practice counting patterns after they have had time to conceptualize the pattern.

I say all of that to set up this next 3 Act task.  I thought, a predictable sequence would be fun, but I want to start out with a number pattern that encourages students to think about the nature of patterns.  For that reason, there will be two different videos for Act 2 based on student responses to what information they need.  The first will give them just the second number and the next will give them the first three numbers.  The goal is to get them to see that patterns cannot be discerned by simple looking at two numbers (or three in cases like the Fibonacci sequence – but that will be explored at a different time:).  There are many standards this task addresses, it can be used at any grade for MP 8.  Or for content standards in several grades in Operations and Algebraic thinking.  Specifically 2.OA.A.1.

Star Pattern Google Slide Deck

Act 1

 

What do you notice?  What do you wonder?

What is the number on the yellow star?

Estimate. 

Act 2.0

 

What do you know?  What do you need to know?

2.1

 

Are you confident in your answer after seeing this new information or would you like to revise?

Act 3

 

3 Act: Jump Drive

While at the NCSM Conference in San Diego, I wanted to see as much of the city as I could after sessions were out.  I walked along the bay and as I continued to walk, I kept seeing scooters and bicycles parked at random intervals.  I decided to check it out and ended up renting one.

CCSS 5.NBT.B.7

Act 1:

IMG_5638Jump Drive Act 1

What do you notice?  What do you wonder?

Focus Question: How much did it cost to rent the bike?

Act 2:

More Information

Act 3:

Jump Drive Act 3

Jump Drive Act 3 (1)

3 Act Math: Pretzel Cut

This task is a little different than most, but I really think it has some good exploration built in and it lends itself to more of an open task.  The standards that I think best fit this task are Math Practice 1, 3, and 4.  If you think there is a good fit with a content standard, please comment below.  There is definitely some partitioning of the whole which could be a good application of 3.GA.2.

Act 1

What did you notice?  What do you wonder?

Focus Question: How will the bread be cut?

Act 2

I made 7 cuts.  Number of Pretzels

Act 3

3 Act: Ho Ho Ho

I happened upon some Little Debbie snacks at the grocery store a few days ago and got some ideas for some new tasks.  This task is meant to show fractions as division by dividing the number of Ho Ho’s by the number of plates (or people).  The common core standard this best fits is 5.NF.B.3.

Act 1

What do you notice?  What do you wonder?

Focus Question: How many Ho Ho snacks will each person (or plate) get?

Act 2

More Information

Act 3