Mathematical Mindsets Chapter 7

From Tracking to Growth Mindset Grouping

Welcome to Week 7 of our Mathematical Mindsets book study! Chapter 7 addresses a very traditional approach to higher level mathematics, and provides significant research against it. The topic is Ability Grouping. Have you heard of it? Have you experienced it, either as a student or as a teacher? I most certainly have, and Dr. Boaler’s research lines up so well with things that I’ve experienced with ability grouping, and she’s opened my eyes to effects I hadn’t really thought of before.

Dr. Boaler, along with an arsenal of research, argues that ability grouping is detrimental to a growth mindset. Grouping students at an early age into low, medium, and high achieving math classes not only hurts the self-esteem of the students in the “low” group; it also denies them the opportunity to ever achieve certain high-level math courses, since their “remedial timeline” is already mapped out and only reaches so far by the end of high school.

Ability grouping also creates a fixed mindset in the students who are in the “high” groups. If they believe they are naturally good at math, when they eventually come to a point where they struggle, they will be less likely to persevere.

Teaching ALL students to have a growth mindset towards math is key. Dr. Boaler shares several strategies and examples of teaching math to heterogeneous groups in a way that fosters growth in all students and allows students to take multiple pathways of achievement. Below, I share some that I am planning to implement this school year.


Open-ended math tasks

When working with students at a variety of levels, open-ended math tasks are key. These “low floor, high ceiling” tasks, as Dr. Boaler describes them, allow students to build a solid foundation and take the skill to as complex a level as they are willing and able to. I needed some more input on what exactly classifies a quality, open-ended math task, so thankfully Dr. Boaler pointed out a few places to look!

The first is part of the UK’s Nationl STEM Centre, and is a collection of task cards that are designed for mixed-achievement groups. These cards are part of a project called Secondary Mathematics Individualised Learning Experinece, or SMILE! Some of the wording will need to be changed, as they were made for students in London, but I have already found some great resources to use during our first unit on Decimals. I definitely need to remember to change things beforehand, though, or my kids will look at the word form of 0.7 and go “What the heck is “nought point seven,’ Miss G.?!”
I encourage you to visit this website and check out the extensive library of SMILE cards and other STEM resources. It’s free to sign up for login access to download the materials.

Another resource that has yet again proved useful is the YouCubed math website. Below is a link to a perfect example of a “low floor, high ceiling” task, which allows kids to explore different ways of approaching the problem, and allows them to go as in-depth as they are able.




This Ice Cream Scoop problem is also the perfect way to introduce multidimensional values, which Dr. Boaler shares as another key aspect of heterogeneous teaching. Allow for, value, celebrate, and assess multiple ways of thinking about and approaching mathematics! 

Don’t focus solely on performing calculations, but encourage students to “ask good questions, propose ideas, connect different methods, use many different representations, and reason through different pathways” (Boaler 121). And remind students regularly that “No one is good at all of these ways of working, but everyone is good at some of them.” This mindset will set the tone for group work that shares responsibility and is respectful of everyone’s thinking.


Roles and Shared Responsibility in Group Work

Dr. Boaler recommends spending a significant amount of time and effort at the start of the year teaching students how to effectively and appropriately work in groups. She shares many strategies for this, but the ones that I am ready to jump right into are:
  • ·         Work with students to carefully develop group norms of respect and listening

o   Create posters of what students do and don’t like other group members doing when working together. This provides student awareness and ownership over norms that we would give anyhow, such as not letting one person do all the work and tell everyone else the answer, saying things like “this is easy” when it may be confusing to some, leaving people out of discussions, etc.
  • ·         Assign roles for students in groups that allow them to balance the workload and equitably participate. Roles such as Facilitator, Recorder/Reporter, Resource Manager, and Team Captain can categorize specific jobs that must be done and questions that can be asked to stem discussion.
  • ·         When assessing group work, assess only one randomly selected group member’s verbal or written response. If they cannot clearly articulate the way their group found the answer, the group must reconvene and continue discussing until every group member clearly understands the concept. They can let you know that their ready to be reassessed, and you ask the same student to explain. Check out Tried and True Teaching Tools' awesome Role Cards created from the roles Dr. Boaler shares - Kathie did an AMAZING job on these, and I will definitely be using them! 
I am so grateful for this book study, and the way in which this book is opening my approach to teaching mathematics! I hope you will join our conversation here in our blog hop comments, or in our Facebook group at Mathematical Mindsets Book Study Facebook Group{request to join, we’d love to have you!}

If you’re interested in some of the research cited in this chapter, I’ve linked some of Dr. Boaler’s studies below.


  1. Thanks for the shout-out, Lorraine :) I LOVE the youcubed site also!! It's such a wealth of information!! And I downloaded the SMILE cards, too. This book study has made me SO fired up about teaching math again!!

  2. I love that you're planning to implement some of the strategies. I can't wait to read more about your journey!