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.
ONE
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.
TWO
Multidimensionality
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.
THREE
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.
