Skip to main content

### What's Math Got to Do with It? - Chapter 3

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

In Chapter 3, Boaler describes two successful approaches that offered students experiences with real math work. These approaches were used in studies that Boaler conducted. The study details that she shares are very interesting (I love reading about research), and I've included the highlights here.

Boaler calls the first approach the Communicative Approach. She completed a four-year study, following about 700 students in three different high schools, to determine that this is a successful approach. Students at one particular school were detracked, algebra became the first course that all students took when entering high school, and the teachers met over several summers to design/alter their courses. In this approach the focus is on "multiple representations," like words, diagrams, tables, symbols, objects, and graphs. The students at this school explained their work to each other, and moved between different representations and communicative forms. Interestingly, these students defined math as a form of communication, or a language.

The students taught with this approach worked in groups and were taught that they are all smart, but have different strengths in different areas; everyone had something important to offer. The teachers involved in this approach reinforced the idea that being good at math involves asking questions, drawing pictures and graphs, rephrasing problems, justifying methods, and representing ideas, in addition to calculating. They also followed an instructional design (called complex instruction) that made group work more effective and promoted equity among the students. Students at this school learned to appreciate the differences in one another.

In comparison to the students in the other, more suburban high schools in the study (using traditional teacher-lecture methods), the students at this urban school ended up outperforming the others on algebra and geometry tests by the end of the second year of high school. By their senior year, 41% of the students in the urban district were taking precalculus and calculus, compared to 23% at the other schools.

The other approach Boaler describes is the Project-Based Approach. Students in two schools were followed for three years in this study, which included the observation of hundreds of hours of lessons, interviews with and surveys of students, as well as various assessments. As the name indicates, students in this group worked on projects that addressed math as a "whole" rather than as separate areas of math. In many cases, students were taught certain methods when they needed to use them in the course of a project, rather than being taught the concepts beforehand. For example, in a particular area-related project, some students ended up needing to use trig ratios, so the teacher taught them about trig ratios.
The projects were open enough that students could go in different mathematical directions - directions that interested them. Students could choose who to work with, so some worked alone, some in pairs, and some in groups.

The students at this school viewed mathematical methods as "flexible problem-solving tools," and ended up scoring higher than the national average on their exams, taken at age 16. For more details, you may want to read the book Boaler has published about this study - Experiencing School Mathematics.

As a result of her studies, Boaler concludes that students need to be actively involved in their learning and they need to be engaged in a broad form of math.

Do any readers use a project-based approach to teach math? If so, how does it work for you?

### Differentiation and the Brain - Introduction

It's summer-time and time to get some reading done! Myself and my Tools for Teaching Teens collaborators are going to read and review Differentiation and the Brain, How Neuroscience Supports the Learner-Friendly Classroom , by David A. Sousa and Carol Ann Tomlinson.We will each be reviewing different chapters, and those blog posts will be linked together as we go. If you're interested in learning more about this book, check back and follow the links to the different chapters:) I'm going to give a quick review of the book introduction here, and then later today I'll be reviewing Chapter 1. According to the authors, differentiation is brain-friendly and brain-compatible! They describe the rise, fall, and rise of differentiation, starting with the one-room schoolhouses, where teachers taught all subjects to all students, of all ages, and HAD to differentiate - there was no other way! As the country's population grew, public schools grew, and students were separat

### Love to Doodle (and a freedbie)

Exponents Color by Number For most of my school life as a student (and even as an adult, during PD), I have really liked doodling! During lectures, discussions...it would help me focus, but also give me something to make me look busy, so I wouldn't get called on in class! I always hated being called on and almost never participated voluntarily:) I liked to draw cubes, rectangles, squiggly lines, etc, and color in different parts of the doodles. Download this freebie:-) I really wanted to make some color by number activities. Since I am not good at creating actual pictures, I decided to make my color by numbers similar to my random drawing/doodling. My Exponent Color by Number is most similar to my past doodles, but I thought it was a little too random, so I started using actual shapes. The Integer Operations Color by Number (freebie), as well as most of my other color by numbers are more structured, but so much fun for me to make! Computerized doodling! Anyone else