Mathematical Mindsets by Jo Boaler
|
Maths is a content area that gets a lot of attention. The attention usually amounts to new ways of presenting material so that kids can "learn" more math and recall more computational functions for an exam.
Thankfully, there are researchers like Jo Boaler and books like Mathematical Mindsets to refocus our attention on what really matters - asking questions and having conversations about pathways to solving problems. It's not about getting to the rigth answer faster than everyone else. It's not about you being ro not being a "Maths Person" or having/not having the "Maths gene". There is no Maths gene! We need to stop saying things like this and perpetuating this belief that some people can or cannot do Maths. Stop It! |
Conrad Wolfram says to "stop teaching calculating" and "start teaching math." We don't need to teach calculation or computation, that's why we have calculators and computers! We need basic numeracy and a connection to the beauty of mathematics. Maths are used in many different fields to make models of the real world. Wolfram talks about four parts of Math:
This is not what happens in most Maths courses. Students learn by formula, practice calculations, and ask, repeatedly, "Why am I learning this?" or "When am I going to use this in the real world?"
I am not disparaging numeracy and mental math. We do need a grasp of basic Maths in our lives. But to grasp the Beauty of Maths, we need to rethink how it is presented and taught. And don't get me started on homework - complete odd #'s 1-31 on pages 96-98, AHHHH!
"Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people." (pg 59)
The exemplar problems shared in the case studies helped me to visualize what mathematics inquiry and student-driven discussions can look like in a classroom that embraces a Mathematical Mindset. Reading through the problems presented in each case had me personally trying ot work through the solutions. I loved the low floor/high ceiling aspect to each problem.
There is also a process for teachers to follow that helps them turn traditional questions from existing curricula into newer and better learning opportunities with a series of questions used to reframe the tasks:
The myth of mathematically gifted children (and adults) are addressed. Many strategies for teaching heterogeneous groups effectively are shared in Mathematical Mindsets. It celebrates students as self- and peer-assessors. Even better is the researched back explanations that state exam scores go up when students are given an opportunity to learn through complex tasks and problem-based learning. Add to this the research that I have read time and again that GRADES DON'T HELP STUDENTS LEARN, and I was grinning ear-to-ear.
"My recommended solution is to assess less; if teachers replaced grading weekly with diagnostic comments given occasionally, they could spend the same amount of time, eliminate the fixed mindset messages of a grade, and provide students with insights that would propel them onto paths of higher achievement." (pg 143-144)
The appendices are loaded with references to scholarly articles, tools for teaching, and activities for students. Let's all embrace the Beauty of Mathematics and embraces our inner mathematician. We are ALL math people!
- Posing questions (learner involved)
- Modeling the real world with mathematical models (learner involved)
- Performing calculations (computer involved)
- Moving from mathematical models back to the real world to answer the question from #1 (learner involved)
This is not what happens in most Maths courses. Students learn by formula, practice calculations, and ask, repeatedly, "Why am I learning this?" or "When am I going to use this in the real world?"
I am not disparaging numeracy and mental math. We do need a grasp of basic Maths in our lives. But to grasp the Beauty of Maths, we need to rethink how it is presented and taught. And don't get me started on homework - complete odd #'s 1-31 on pages 96-98, AHHHH!
"Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people." (pg 59)
The exemplar problems shared in the case studies helped me to visualize what mathematics inquiry and student-driven discussions can look like in a classroom that embraces a Mathematical Mindset. Reading through the problems presented in each case had me personally trying ot work through the solutions. I loved the low floor/high ceiling aspect to each problem.
There is also a process for teachers to follow that helps them turn traditional questions from existing curricula into newer and better learning opportunities with a series of questions used to reframe the tasks:
- Can you open the task with multiple methods, paths, and representations?
- Can it be made into an inquiry task?
- Can the students explore the problem before learning the methods?
- Can there be a visual component?
- Does it have a low floor and high ceiling?
- Can you add requirements to convince and reason?
The myth of mathematically gifted children (and adults) are addressed. Many strategies for teaching heterogeneous groups effectively are shared in Mathematical Mindsets. It celebrates students as self- and peer-assessors. Even better is the researched back explanations that state exam scores go up when students are given an opportunity to learn through complex tasks and problem-based learning. Add to this the research that I have read time and again that GRADES DON'T HELP STUDENTS LEARN, and I was grinning ear-to-ear.
"My recommended solution is to assess less; if teachers replaced grading weekly with diagnostic comments given occasionally, they could spend the same amount of time, eliminate the fixed mindset messages of a grade, and provide students with insights that would propel them onto paths of higher achievement." (pg 143-144)
The appendices are loaded with references to scholarly articles, tools for teaching, and activities for students. Let's all embrace the Beauty of Mathematics and embraces our inner mathematician. We are ALL math people!