Math-ish: A Groundbreaking Guide to Finding Joy and Understanding in Mathematics

by Jo Boaler

From Stanford professor, author of Limitless Mind, youcubed. org founder, and leading expert in the field of mathematics education Jo Boaler comes a groundbreaking guide to finding joy and understanding by adopting a diverse approach to learning math.

“Every once in a while, someone revolutionizes an approach to a difficult subject and changes it forever. That is what Jo Boaler has done for math. Fresh, smart, and inclusive, Jo Boaler's strategy eschews the one-size-fits-a-few approach and instead allows math to be seen and solved by everyone. A huge achievement. Math-ish is the only math book I’ve ever enjoyed reading in my entire life. Honestly.” -Bonnie Garmus, author of Lessons in Chemistry

Mathematics is a fundamental part of life, yet every one of us has a unique relationship with learning and understanding the subject. Working with numbers may inspire confidence in our abilities or provoke anxiety and trepidation. Stanford researcher, mathematics education professor, and the leading expert on math learning Dr. Jo Boaler argues that our differences are the key to unlocking our greatest mathematics potential.

In Math-ish, Boaler shares new neuroscientific research on how embracing the concept of “math-ish”—a theory of mathematics as it exists in the real world—changes the way we think about mathematics, data, and ourselves. When we can see the value of diversity among people and multi-faceted approaches to learning math, we are free to truly flourish. Utilizing the latest research on math education, Jo guides us through seven principles that can radically reframe our relationship with the subject:

• The power of mindset on learning

• Utilizing a visual approach to math

• The impact of physical movement and communication on understanding

• Understanding the value of an "ish" perspective - in mathematics and beyond

• The importance of connected and flexible knowledge

• New data on diverse teaching modes that work with different learning styles, not against them

• The value of diversity in learning mathematics—and beyond

When mathematics is approached more broadly, inclusively, and with a greater sense of wonder and play—when we value the different ways people see, approach, and understand it—we empower ourselves and gain a beneficial understanding of its value in our lives.

Genres: Nonfiction, Mathematics, Education, Science, Teaching

304 pages, Hardcover

Published May 7, 2024

About the author

Dr Jo Boaler is a Professor of Mathematics Education at Stanford University and co-founder of www.youcubed.org. Formerly the Marie Curie Professor of Mathematics Education for England, a mathematics teacher in London comprehensive schools and a researcher at King's College, London. She is the author of eight books including What's Math Got To Do With It? (2015) and Mathematical Mindsets (2016). She is the recipient of the NCSM award for equity, the author of the first MOOC on mathematics learning for teachers and parents, a White House presenter and an advisor to the PISA team at the OECD.

Reviews

[Willem Hoekstra · Rating 4 out of 5]

Overtuigend pleidooi voor wiskundeonderwijs dat betekenisvol is, gericht op begrip en op wiskunde als menselijke activiteit, en het belang benadrukt van productief worstelen.
Wat mij minder overtuigde waren de neurowetenschappelijke bewijzen voor zaken die voor mij veeleer een pedagogische verklaring of overweging hadden.

[Shai · Rating 5 out of 5]

“…the most productive times for our brains are when we are struggling and making mistakes”.

I first heard of Jo Boiler about eight years or so ago when her videos about mindset and creating a math community were on YouCubed. I used those videos to set up my math class’s community agreements.

In Mathish, Boaler makes the case for a change in the way that we teach mathematics to children. The typical way mathematics is taught is devoid of diversity - it’s dependent on formulas and procedures and only one “right” answer. In Mathish, Boaler stresses the value of struggle and of math diversity and “ish” - concepts she explains in the book.

The takeaway I got from this book is that we need to step away from teaching math as it has been in the texts. We need to give our students challenges and allow them to work on these challenges before we even begin to talk about them. Allow them to have a productive struggle and work in teams prior to us jumping in and “saving” them with a lesson. There is value in making mistakes and we should envelop our students’ thinking around that concept early and often.

I would recommend this book to parents, teachers, high schoolers who can read an analyze the text or just anyone wanting to know more about math and growth mindsets.

I received a copy of this Advanced Reader Copy (ARC) via NetGalley thanks to HarperOne.

[Alexander B · Rating 1 out of 5]

Look. I haven’t read this book and I’m not going to because the author amply demonstrates that she doesn’t know basic arithmetic!! Examples include amazing formulas like 2/3 * 2=4/6 and countless others. It’s irrelevant that this formula appears as part of some “ish” method that gives correct results. The formula is wrong according to any actual mathematician. It’s pathetic that anyone would give this more than one star.

[Jay Roche · Rating 3 out of 5]

I appreciate most of what Jo Boaler is trying to do. I see from working in the classrooms that many middle school students come in with no number sense. Math is one of, with ELA, one of the most fundamental, yet hated, classes. We do need a change. A lot of what Boaler says makes sense-ish. The discredit of “narrow math,” unfortunately, doesn’t make a lot of sense. Route memorization of basic fact fluency is discredited and has forced many school districts to abandon the practice. The result is a population of middle school students who struggle with algebra and geometry because they can’t add, subtract, multiply, or divide single digit numbers adequately. The cognitive science suggests that automaticity in single digit facts impacts a student’s ability in more complex math. It seems like her all or nothing approach would be better suited to a multifaceted approach that uses multiple methods of learning instead of relying on just the visual. They are both important.

[Jeanne Sumiko Wong · Rating 5 out of 5]

This book was the perfect water for my depleted soul after teaching 6th-grade math this school year. I am inspired to keep going, find creative ways to engage the curriculum, trust the investigation and discovery of students, and believe in my warrior mindset. Math is magical and this book reminds me of that!

[AANVI WRITES · Rating 4 out of 5]

Mathish by Jo Boaler is a book that changes your perception towards the most feared subject Mathematics. Most of us fear the word math because we fail to understand the concepts. Jo has tried to put an end to all these fears of the subject by making concepts accessible and understanding the logic .

Boaler explains how math is an integral part of everyday life and introduces simple and easy-to-understand concepts. The book is filled with her experiences, valuable tips, innovative concepts, and practical strategies for parents and educators to use in their children's development and careers.

What I liked about the book is its fresh ideas, which emphasize that math is for everyone and that creativity and math can coexist. Boaler supports her points with various examples, graphs, tables, and visual concepts. The author emphasizes the importance of visual learning and how it aids innovative problem-solving, ultimately breaking traditional notions of math.

Overall a book that changes the perception towards math.

[AJ · Rating 5 out of 5]

I read this book for a work training and it honestly changed my outlook on teaching math. I teach a one-marking period course four times a school year, and I decided to switch up how/what I taught in the middle of the school year instead of waiting until next year. There were even a few examples in the book that made me understand a concept better - for example, multiplying and dividing fractions! The success stories from Boaler’s former students were inspiring! Basically, if I were to summarize concisely, kids learn much better, and truly understand, by exploring patterns and making observations (even Calculus!) rather than memorizing rules and formulas.

[John Mauro · Rating 1 out of 5]

Yikes. This is a book on math pedagogy where the author makes elementary errors in multiplying fractions:

[Jahn Alexander · Rating 1 out of 5]

It's basically 300 page ad for her education program and website. If you want to learn about how we learn I HIGHLY recommend "A mind for numbers" by Barbara Oakley which focuses much more on how the brain works and remembers new and difficult concepts.

[Heidi Green · Rating 4 out of 5]

Although I’m not sure I agree with everything presented, this book definitely made me think.

[Angelee · Rating 4 out of 5]

The last 15 pages of the book were a bit weird and not what I was looking for from this book. There were many other parts that were interesting and motivating.

[Debabrata Mishra · Rating 4 out of 5]

Dr. Jo Boaler's "Math-ish" heralds a paradigm shift in the world of mathematics education, merging cutting-edge neuroscientific insights with an inclusive pedagogical approach. This book aims at debunking the seemingly omnipresent phobias about mathematics and attempt to convince the reader that ones’ so-called weaknesses are strengths that make for producing extraordinary mathematicians.

She explains in full detail how a change of attitude translates into a dramatic change in the performance on mathematics. Through embracing a growth mindset learner becomes free from the alledged limitations. From Carol Dweck’s initial research in mindset, she posits that growth mindset does offer guard and helps drive learners to more accomplishments.

The book also seeks to remind about the forgotten value of visual learning in mathematics. Also, her support of the use of visual aids and tools including graphs, diagrams, and spatial reasoning tasks, shows a lot of appreciation of diversity in human learning. On this basis, she argues that, visual learning aids not only improve understanding but also increase creativity and innovativeness in solving problems which is well supported by modern research in cognitive science. Her work of addressing the effectiveness of the ideas of working knowledge through movement and paraverbal communication is revolutionary.

The most credited to her invention is the use of the term “ish. ”It summarises the concept that being able to get an exact answer is not the only way of being good at maths. By focusing on approximation, estimation, and loose thinking, she releases learners from the rigorist’s straitjacket. This is as with life problems that often an approximate solution is reasonable since exact results are not always possible. Hence, her “ish” philosophy promotes a more inclusive and tolerant atmosphere towards mathematics.

In conclusion, the work is a masterpiece that breaks traditional standards of mathematics education. Her analytical expose and principles expounded here are a source of hope to the learners and educators. It is more than an encyclopedia of pedagogy, but a declaration of the need for a better educational system.

[Cheryl · Rating 5 out of 5]

Jo Boaler roots all of her pedagogical advice in science, research and data. She presents it in such an accessible and inspirational way. Some of this book felt redundant as I follow her work closely and have read her previous works. Still, there were some practical take aways and I recommend this to all math educators.

[Marwa · Rating 5 out of 5]

I would love all educators , schools and teachers to read it. I’m grateful for some teachers that have crossed my path, as much as people looked at them as not “normal” this book proved that they were in the right path.

[Meg · Rating 5 out of 5]

Fantastic! I’m a high school math teacher and read this to get myself back into school mode heading into the year. It exceeded my expectations; not only do I feel fired up to get back to teaching, but I also got so many good activity ideas from this book!

[Annie · Rating 5 out of 5]

Originally posted on my blog Nonstop Reader.

Math-ish is a well reasoned evaluation of math learning and new ways to *think* about math education and how people learn, by Dr. Jo Boaler. Released 7th May 2024 by Harper Collins on their HarperOne imprint, it's 304 pages (print version) and is available in hardcover, audio, and ebook formats. It's worth noting that the ebook format has a handy interactive table of contents as well as interactive links.

The author has a long career in education and presents her experiences showing the differences in results for students who succeed and those who struggle. Many educational teaching methods haven't changed a whole lot in hundreds of years. Outdated methods are slowly being replaced but change has been slow and often ineffective. Currently mathematics classes are being stripped to the bare minimum due to funding cuts as well as a lack of qualified and engaged teachers. All of this has led to a significant decrease in mathematics competency for students in all stages of education.

Additionally, the lack of diverse tailored methods has led directly to a lack of diversity. The past modality for teaching mathematics has proven inadequate for our current educational needs. The author makes a very good points for individual structure and creativity in mathematics education to reach more students of all backgrounds and actually *teach* them, helping them build their own problem solving tools instead of just using cookie-cutter tests to "cram - test - forget". The author also covers assessment methodology and feedback for reinforcing learning and helping students retain the skills they've acquired.

The text is well annotated throughout and the chapter notes will provide readers with a wealth of further sources. It's layman accessible, but information dense and a niche subject (but of course STEM education and competency are absolutely vital to our continued existence on the planet).

Four and a half stars. Definitely a good choice for public and school library acquisition, educators, and others involved in teaching mathematics.

Disclosure: I received an ARC at no cost from the author/publisher for review purposes.

[Alicia · Rating 4 out of 5]

Boaler's stance is that we need to change the way we approach math- from the start. I definitely agree so this was an easy book to "sell" me on because I am in the camp that she discusses early on that my emotions of not being good at math paint my entire world regarding math that began from not being good at those times table timed tests and continued from there. The silver lining I tell people is that I need the practicality-- percentages to know the discount on clothes that I'm going to by and fractions when I'm baking-- but the open mindedness of conversation, the perspective that there was plenty of ways to solve a problem, that math diversity / math-ish needs to be the approach that overhauls the system. So I'm biased in that I want to get behind what she shares. I'm trying to get my husband- a computer science major with a math minor- to read it too to see what he thinks.

Boaler approaches it with organization and easily understood principles. My only annoyance was that she dropped her connection to Stanford more times than I could count-- got it, you're super smart and taught at Stanford, please move on-- not to discount it but that she included it often. I applaud her work with youcubed to test out these theories and put the research where her mind was going. Plenty of people need to read this book especially those in education!

"One of the most important goals we should hold for our students learning to be citizens of our diverse world is this form of respect for their fellow students, no matter their race, class, gender, achievement level, or any other form of difference.... he demonstrated how educators can encourage thoughtful metacognition in their students. Watching a teacher in the first week of the school year is always incredibly informative, as this is the time when teachers establish what will be the norms of their classrooms for the year ahead."

"Simplify... "For example, when asked to add 19 + 6, some students instead add 20 + 5. This may seem like an obvious strategy, but I have found that many low-achieving students believe that it is somehow "not allowed" to change the problem that is given to them. The approach of changing numbers or shapes helps people become more flexible in their problem-solving."

"Learning to learn; encourage struggle; concepts and connections; multiple representations; diverse practice and feedback."

[Sindhu Vinod · Rating 4 out of 5]

What caught my attention first was the colorful and vibrant book cover that screams pick me up. As someone who was paranoid about the subject mathematics in School and College though I had a handful of eminent mathematicians in my family in somehow the subject failed to give me that sparkly eye. A few pages into the book I realized why didn’t this book come up when I was studying. This would have made a difference in the way that Mathematics was being taught in Schools.
The Author has thought of and put forth the idea that not one size fits all when it comes to approaching mathematics. Celebrating the various ways how people approach mathematics and coining the term math-ish was brilliant.
In the first chapter, the Author meets a CEO wherein her friend arranges a meeting to discuss ideas where she can propose ideas to improvise the ways of teaching mathematics by introducing him to diverse ways of understanding a mathematical problem which became the ice breaker. This chapter gave me an idea of what to expect in the remainder of the book. The second chapter that goes by name Learning to Learn explores methodologies taken by mathematically empowered people to analyze problems that help them succeed, those methods which they would have acquired from friends or family.
To make the content relatable and engaging the author shares real-life snippets from her teaching experiences. Neuroscientific research insights are also shared on how maths is processed by the brain. She lists down the seven principles which will transform the way you look at math.
The book will empower you to see math as a joyful and accessible discipline. Whether you are a student, teacher, or someone who is a curious learner this book will defiantly change the way you approach mathematics.

[Pavireads · Rating 5 out of 5]

Unlock creativity, embrace diversity, and transform math anxiety into joyful learning with 'Math-ish' by Jo Boaler. Discover seven dynamic principles to reframe your relationship with math.

This riveting book offers seven principles that dynamically reframe our relationship with the subject. Check the next slide for these seven principles. Moreover, it engages readers with picturesque representations that boost confidence, knowledge, and the potential for a metacognitive approach, helping navigate their mathematical journey towards a positive relationship with the subject.

Boaler also discusses new research about the mathematical approaches needed in the modern world.The metacognitive approach enhances problem-solving skills, particularly as mathematical content becomes more advanced. This method helps prevent students from feeling excluded and maintains their interest and performance in mathematics as they progress through their education.

This book is perfect for teachers, parents, and students, inspiring them to see math in a whole new light, making it engaging, accessible, and achievable for all.

[Ann Williams · Rating 5 out of 5]

I read Limitless Minds several years ago and was excited to read this book. I found it fascinating. I listened to the audio book so did not have the tables and charts throughout the book as my library did not provide ‘the enhancement’.

I found that I wished I could go back to my school years and relearn math this way, despite being ‘good at math’. Diversity is needed in all aspects of life, but diversity in looking at math is needed to be taught as a good thing, something that can be open to discussion.

I found the discussion on grouping items together (up to 4) intriguing. I thought we all grouped things quickly but hearing how this skill is not taught to some kids and then they don’t do as well as a result in math an amazing easy thing to teach and learn. Also the idea of estimating(she had a different word) interesting. Before you work out the answer, what approximately should the answer be- thereby using the logic side of your brain and then helping you solve it. I love the ‘ish’ concept and I realize I do it all the time!

It is crazy that people find her ideas controversial. These concepts appeal to common sense, something most lacking today.

[Chris Jaffe · Rating 4 out of 5]

This book was valuable and helped me approach how I teach some of my classes - which is wild because I teach history, not math.

Yeah, but some ideas are applicable, like an early chapter that spoke of metacognition, making students aware of why they were asked to learn some material and what value it has. This can make them more willing to partake in learning it and help them focus more on it. Boaler describes it better and more detailed than I do right here, but that's a general gist. I mean, I've heard this before and known it, but sometimes in teaching you can get too caught up in the process and it helps to have the bigger picture reframed for you.

There are a lot of other parts of the book here, and I skimmed over some of it, but it's still a valuable educational resource.

[Sammy Stitt · Rating 3 out of 5]

maybe i’ve just read too many math books. the points she presents are interesting and agreeable- metacognition, resilience in the face of failure, tailored feedback, group work, recognizing differences in perception- these are all important and valuable in the process of learning math, but i feel like these points could’ve been effectively summarized in a tenth of the time. I appreciated the research and neuroscience behind her claims, i did, but i don’t know, i’m not sure there was enough substance of that to make a 300 page book. the chapters seemed long and if she was going to present her claims in such a logical “if, then” format, it didn’t need to be a book. I always feel bad about being a hater on goodreads, but, yk.

[Rebeca · Rating 4 out of 5]

I wish I could be more enthusiastic about this book. For me it's a 3 star but I am giving it 4 because it's good, it's just not for me. I have been pretty obsessed with new math, and Jo Boaler is the person behind it. I live that we can think on new ways about math and bring in the theoretical and visual at the very earliest stages. My own dyslexic, 100% visual learner kid has responded so well to this style of math. But it's not without controversy, and this book explores not just the math but the death threats that accompanied the new curriculum. At the end of the book I was left thinking about politics, fear of change and how people want to protect access to math and not make learning equitable. Timely.

[Laura Beth · Rating 3 out of 5]

This book is really intended to convince teachers and give them the tools to teach with this style. That’s very cool and it is a good approach, but as an adult who is not teaching math but more interested in learning as a student, it wasn’t what I thought it was going to be. Also I listened to the audiobook on Libby, which didn’t have the visual attachment reference, so quite a number of the points she talked about were at least partially lost because they referenced a visual that wasn’t available to me. Perhaps I’ll give the physical book a read in the future to see if I get more out of it that way.

[David A. · Rating 5 out of 5]

Eye Opening

As a developmental pediatrician who often advises parents and teachers of children with learning differences, this book opened my eyes to a new way of approaching these challenges which will be very helpful to me and my patients. As a parent of a (now grown and highly successful adult) child who was mathematically gifted but often chafed under his instruction during K-12 education, this book gives me a new understanding and perspective on what our family when through all those years ago. Thank you for this book, Jo. I will be recommending it to colleagues, parents, and teachers for years to come.

[Donald W. · Rating 4 out of 5]

Jo Boaler brings everything together so clearly, reinforcing one of the book’s most important themes: the order of instruction matters. One key idea that stuck with me was her suggestion that “a good way to practice the model… is to change the typical order of instruction, so that students get to explore tasks before they are taught new ideas.” That concept challenged how I’ve traditionally approached classrooms in general. It reminded me that when students get to wrestle with a problem first—before being given all the tools—they become more curious, more invested, and more likely to understand the “why” behind the math.

[tanya · Rating 5 out of 5]

An engaging and easy read. Beautifully done. Dr. Boaler does such a lovely job of bringing together stories from so many different parts of her work that inspire the reader with a vision of creative, engaging, and inclusive math learning for all. But she doesn't stop there! I appreciate that the book also gives concrete examples of what creative and diverse math meaning making actually looks like from children to grown adults in and outside of the classroom. I highly recommend this book!! I'd give it 6 stars if I could!

[Hannah Thomas · Rating 4 out of 5]

I love how the author looks at math in many different ways of learning. One person has one way of learning. Another has a different view. They may not be able to look at the same way of learning as the other person. Growing up, I saw math being taught one way and one way only. In college: "it's my way or the high way"

Now a college educator, you don't have to go by exactly one way. Find the learning style that works for you. If one way works, use it. It never hurts to ask your teacher: "would you accept this way?"

[John Borsi · Rating 3 out of 5]

I'm a math nerd, so I wanted more math!

I loved the author's perspectives on math pedagogy and systemic roadblocks to inclusive education. Unfortunately, I think this book falls into a bit of weird spot - not enough math for the math nerds, not enough education for the educators, not enough brain stuff for the biologists, not enough sociology for the sociologists, not enough policy details for the policy wonks.

[Alexandria Avona · Rating 5 out of 5]

Excellent work by Ms. Boaler yet again. She came out about her abuse in this book and it is just horrific. That professors at universities are that pathetic that they take time out of their day to stalk and bully is an embarrassment to the profession.