What’s Math Got To Do With It? Reflections and Thoughts, Part 2

I recently finished reading Jo Boaler’s book What’s Math Got To Do With It? and I need a way to reflect on what I had learned and consider ways to implement her research in my own teaching. This is Part 2 of a (probably) 4-part series.

I’m going to use quotes from the book and expand on them with my own thoughts. Chapters 3 through 6 primarily outline the findings that Jo has gathered from her research over the years, and I’m going to cover Chapters 3 and 4 in this post.

Chapter 3 – A Vision for a Better Future: Effective Classroom Approaches

The Communicative Approach

Jo highlights a school that uses what she calls the communicative approach to teach math. In this approach, students “were given opportunities to work on interesting problems that required them to think (not just to reproduce methods), and they were required to discuss mathematics with one another, increasing their interest and enjoyment” (p. 66). The teachers in particular believed and taught from the point of view that there are many different ways of being “good” at math:

…being good at mathematics involved many different ways of working, as mathematicians’ accounts tell us. It involves asking questions, drawing pictures and graphs, re-phrasing problems, justifying methods, and representing ideas, in addition to calculating with procedures. Instead of just rewarding the correct use of procedures, the teachers encouraged and rewarded all of these different ways of being mathematical.

… Put simply, because there were so many more ways to be successful at [this school], many more students were successful (p. 67).

This is easily the hardest thing for me as a teacher – not to revert back to teaching the way I was taught. I fall into the trap of valuing the fastest way to get things done, I undervalue sense-making in favor of “we have to get through this before the bell rings”, and I allow students to just memorize how to do things. I want so badly to get away from these habits, but it means that I need to replace them with new habits. That’s where I’m struggling. I’m a very detail-oriented person, so when I think about changing aspects of my teaching, I want to be specific: Instead of saying _____, I’ll say _____. Unfortunately, teaching isn’t so prescriptive. I need to catch myself in the act, and think on my feet well enough to make the change.

Side note: Because I know this about myself, I’m going to ask for my students’ help when it comes to mindset this year. I’m going to teach a lesson about mindset and how your brain grows during the first week of school, and I’m already planning to follow it up with this statement to my students: “I have had a fixed mindset my whole life, especially about school. I’m learning how to have a growth mindset along with you guys. Because of this, I sometimes say things that come from my old fixed mindset. When I say those things, I want you guys to call me out on it. If I don’t realize I’m doing it, I can’t fix it, so I need your help to keep making that change.” I’m hoping that a high-school student’s natural love for telling the teacher that she’s wrong will make them very excited about this and help keep me in line.

The Project-Based Approach

I actually didn’t highlight anything in this section, either because I was reading so fast that I didn’t think to stop and highlight, or because there wasn’t a highlight-able (short) sentence available. Basically Jo did studies at two schools which were similar in demographic makeup and location. One was project-based and one was traditional. Spoiler: the students at the project-based school performed better on their national exam and a far higher percentage of them were interested in continuing to study mathematics after secondary school.

Jo states that her studies of the communicative and project-based approaches led to one big conclusion:

students need to be actively involved in their learning and they need to be engaged in a broad form of mathematics – using and applying methods, and representing and communicating ideas (p. 83).

Chapter 4 – Taming the Monster: New Forms of Testing that Encourage Learning

I got very excited when I read the title of this chapter, because I’ve been doing a lot of thinking over the past two years about the purpose of assessment and how to write effective assessments.

What Is Wrong with What We Have Now?

Jo first focuses on standardized tests in the US. The format of the test (multiple-choice problems) and the reporting of scores (ranking students as above-average, average, below-average, etc.) can cause so much damage.

First, multiple-choice tests are not used in the highest-performing countries for 4 main reasons (all from p. 86):

  1. The goal is to assess understanding. In order to do so, you have to look at a student’s work, not at which letter they chose (where it’s possible that none of them mean anything to the student).
  2. Multiple-choice tests are known to be biased. There is some evidence that multiple-choice tests are biased against girls, and there is LOTS of evidence that they are biased against ethnic minority students.
  3. Timed tests create anxiety and contribute to the high levels of stress that our students currently report. (Story of my elementary-school math experience, right here. My mom is nodding her head so hard right now.)
  4. “The best thing that multiple-choice tests show is a student’s ability to complete multiple-choice tests” (p. 86). The SAT is a classic example of a timed multiple-choice test, and do you know what SAT prep courses actually teach? Strategies to choose the best answer in a multiple-choice setting. They really don’t teach much content. (I used to teach them.)

The standardized tests we use in this country don’t test thinking or reasoning, just procedures, so they don’t give us useful information. Furthermore, when we report results, we assign labels to the students. The previous test we used in Arizona reported student scores using the labels Exceeds Standards, Meets Standards, Approaches Standards, and Falls Far Below Standards.

(I could go off on a whole rant here about how these labels make it sound like we’re evaluating students’ performance against a set of standards and un-ambiguously saying that they demonstrated understanding of the standards set for their grade level, but they don’t – they actually compare students to each other. These scores are based on where a student fell compared to other students, not whether they demonstrated understanding of the standards.)

These labels that we assign are damaging to students across the spectrum (the students who did well and the students who did poorly), but Jo points out the effect that this reporting of standardized test scores had on a student that she interviewed, Simon. She came away with this conclusion:

Testing and reporting measures such as those experienced by Simon can create low-achieving students, crushing students’ confidence and giving them an identity as a low achiever.

… If you tell students they are low achievers, they achieve at a lower level than if you do not (p. 91).

If I’d been reading this book with a pen and not a highlighter, I think I might have actually scrawled a very sarcastic “NO SHIT” in the margin.

Another study “found that students who were not given scores but instead given positive constructive feedback were more successful in their future work. Unfortunately, [this study] also found that teachers gave less and less constructive feedback as students got older” (p. 93-94). This isn’t surprising. Feedback isn’t real high on my priority list when I’m grading 90 of the same test. The way we have set up high schools in this country leads to this.

Assessment for Learning

Here’s where I got excited again (which is good, because reading the first half of this chapter is really depressing) – Jo is going to tell us how to assess so that learning continues, not ends, after the assessment.

3 requirements – “Students are made aware of what they are, should be, and could be learning through a process of self- and peer assessment” (p. 96).

What does this actually look like? Clear objectives. Students should understand them, and they should show the relationships between ideas. Those objectives should be used by the students to see what they should be learning from a piece of work. They should evaluate their (and their classmates’ ) work against the objective and see whether they understood what the objective says. In doing so, they come to understand the big picture and they also take ownership of their learning.

Students need to move from being passive learnings to being active learners, taking responsibility for their own progress, and teachers need to be willing to lose some of the control over what is happening, which some teachers have described as scary but also liberating (p. 98-99).

The most important part of the assessment-for-learning approach is in the feedback from teachers. Giving a score is counter-productive because students just focus on the score and not on next steps. Giving feedback (particularly without a score) is the most beneficial in getting students to focus on what they need to do next in order to continue learning.

This is valuable information for me as I’m trying to decide how to assess in my Algebra 1 Support (intervention-type) class this year. Sounds like I need to be careful NOT to write any kind of score on my students’ quizzes, but only feedback. This feedback should consist of commenting on errors with specific suggestions for improvement and include at least one positive remark.

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