FYMSiC Book Reviews

Have you read a wonderful book about mathematics or statistics? Share the book and your review with the FYMSiC community! 🙂

 

Latest Good Reads

♦ Teaching with AI: A Practical Guide to a New Era of Human Learning by José Antonio Bowen & C. Edward Watson

Recommended by Gizem Karaali (Pomona College)

Both authors are well established in the pedagogy sphere, having written a book or more about teaching with technology. So when ChatGPT and its friends burst upon the stage in late 2022, they probably noticed that there would be some need for a book that teaches instructors about the new technology. The book is well organized into three parts. They begin with an overview of AI basics, defining AI literacy, and “reimagining creativity” in this brave new world. The second part focuses on how instructors can use AI in their course prep and touches upon the hot button topics of cheating, grading, and other policy concerns. The third part is more focused on the learning part, and we learn about assignment and assessment design in this new context.

 

♦ Active Learning with AI: A Practical Guide by Stephen M. Kosslyn

Recommended by Gizem Karaali (Pomona College)
 

Kosslyn writes in his introduction that he did not intend to write a book on AI. He was just trying to update his book on active learning for online education. But he found that all five principles he based that book on could be enhanced with the proper use of AI. So instead of revising that other book, he ended up writing a totally new book. Those who read his online education book might find similarities in the two books in terms of organization. Both are organized around the five principles of active learning — don’t worry if you do not know them; he also takes the time to explain them effectively. And for each principle he illustrates with detailed examples how to incorporate AI in pedagogically sound and productive ways.

Both books can be good starting points for faculty interested in thinking about how the new generative AI platforms might impact education. I felt that the first book may have been a bit too hastily prepared for publication, and that it could have benefited from more thorough fact-checking and copyediting. And I felt that the second book showed its origins in a book on active learning strategies. Nonetheless, both books feel pertinent to the moment we are in and are up to the task they set themselves up for. Both have a large number of example prompts for folks willing to play with their favourite generative AI tool, and any instructor willing to think about their own pedagogical goals and aspirations while reading will get much out of either book. None of the examples are explicitly mathematical, but a mathematics / statistics instructor will still benefit significantly from engaging with either book for an extended period of time.

 

♦ The Man Who Counted by Malba Tahan

Recommended by Raphael Camargo Penteado (University of Toronto, OISE) & Asia Majeed (University of Toronto, OISE)

I am sure you have encountered books that upon first reading them made you think, “I wish I knew about this book earlier.” This is exactly what happened to me when I was a 17 year-old student and first came across The Man Who Counted by Malba Tahan.

Some of you might be familiar with the text, as it was originally published in 1946 by the Brazilian engineer and professor Júlio César de Mello e Souza and has achieved significant success, with one hundred editions issued and published in several countries, including the USA. For those not familiar, Malba Tahan is a heteronym used by Júlio César de Mello e Souza, who published many books under this heteronym, all of them set against the backdrop of an Arabian golden-age scenario. In 1972, the book was honoured by the Brazilian Academy of Letters on its 25th edition. Perhaps some of the readers may be asking: “How have I never heard about this before?” This is why I thought this book review would be relevant.

There are not many papers in English regarding The Man Who Counted. We couldn’t find much, neither old nor new publications. In Portuguese, however, there are several publications about the text, including reviews, analysis, and pedagogical contents. So, we read these publications to bring other perspectives about the text and present recent observations and reflections regarding the book in a context of numeracy, mathematical education, multiculturalism, and educational practices. One of the most relevant aspects of the work is the cultural appreciation of an alien culture by a Brazilian-born author with no close relations to the Persian culture. The choice to set his storytelling narrative in the Middle East, and to adopt a Muslim mathematician as his protagonist, underscores a profound respect and appreciation for cultural diversity. This approach can be seen as an illustration of Gay’s (2010) culturally responsive teaching, which encourages using the cultural knowledge, prior experiences, and performance styles of ethnically diverse students to make learning more appropriate and effective for them. The stories within the book, such as the three sailors’ problem diving a thirty dinars diner bill in a way that they end up with a five dinars refund, not only introduce mathematical problems but also immerse readers in cultural and ethical considerations. While The Man Who Counted can be lauded for its cultural appreciation, it is essential to approach its storytelling with a critical eye, ensuring that they serve as bridges rather than barriers for students from diverse backgrounds (Ladson-Billings, 1995).

As someone who finds immense beauty in mathematics, I see its allure not just in its abstract elegance, but also in its practical applications and the stories that surround it. Teaching fractions, a concept fundamental to math, feels as enchanting to me as solving The 35 Camel Problem. Even when I’m guiding adults, I understand the importance of capturing their interest in fractions. I firmly believe in intertwining mathematical concepts with real-world narratives to create a captivating learning experience. Through storytelling, I strive to bridge the gap between abstract theories and tangible examples, making mathematics more accessible and engaging. Whether it’s exploring the division of resources among camels or breaking down a pizza into equal slices, the relevance of fractions becomes vividly apparent. By fostering connections outside the confines of the classroom, I aim to infuse mathematics with a sense of relevance and intrigue, enriching the learning journey for students of all ages. In doing so, mathematics transcends its traditional boundaries, transforming into a rich tapestry of narratives and connections that deepen our understanding of the world. This philosophy is beautifully encapsulated in the book The Man who Counted I recently read, which emphasized the power of storytelling in teaching math, further reinforcing my belief in this approach.

In conclusion, we should point out that the tales of Beremiz Samir address many aspects of numeracy by revealing some interesting thoughts and perspectives of the character regarding the understanding of his reality using numbers. Considering that the storytelling pedagogy finds its roots in social interaction and culture, in a socio-cultural manner, as proposed by Vygotsky (1978), the narratives of Beremiz Samir’s adventures assert that any subject matter can be taught effectively in some intellectually honest form to any child at any stage of development (Bruner, 1996). Tahan takes this to heart, presenting mathematical concepts through stories that are accessible and engaging for learners of various ages and stages.

References

1. Boaler, J. (2002). Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and Their Impact on Student Learning. Lawrence Erlbaum.
2. Bruner, J. (1996). The Culture of Education. Harvard University Press.
3. Gay, G. (2010). Culturally Responsive Teaching: Theory, Research, and Practice. Teachers College Press.
4. Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465-491.
5. Tahan, M. (1993). The Man Who Counted: A Collection of Mathematical Adventures. W. W. Norton & Company.
6. Vygotsky, L. (1978). Mind in Society: The Development of Higher Psychological Processes. Harvard University Press.

 

♦ Mathematics for Human Flourishing by Francis Su

Recommended by Xiong Wang (University of Alberta)

Francis Su’s “Mathematics for Human Flourishing” transcends the boundaries of a traditional mathematics book. It is a profound exploration of the deep connections between mathematics and human life, offering a refreshing perspective that invites everyone to ponder the significance of math in our lives. At its core, Su’s book is a testament to the intrinsic virtues of mathematics. He artfully weaves together personal anecdotes, historical insights, and mathematical concepts to illustrate how math is not merely a tool for solving equations, but a pathway to deeper understanding and appreciation of the world around us. Through engaging narratives and thought-provoking reflections, Su reveals the humanistic side of mathematics, showing how it can enrich our lives and foster a sense of wonder and creativity. Su challenges the prevalent notion that math is solely the domain of the intellectually gifted, arguing instead that it is accessible to all. He advocates for a more inclusive and compassionate approach to teaching and learning mathematics, one that values curiosity, perseverance, and empathy over rote memorization and standardized testing. Furthermore, Su delves into the ethical implications of mathematics, exploring how it can be used both to empower and to oppress. He confronts issues of social justice and equity in mathematics education, urging readers to consider the ways in which mathematical knowledge can be harnessed for the betterment of society. In conclusion, Mathematics for Human Flourishing is a captivating and thought-provoking book that challenges conventional notions of mathematics and inspires readers to cultivate a deeper appreciation for its profound significance in our lives. Su’s blend of mathematical insight, personal reflection, and social commentary makes this book a must-read for anyone interested in mathematics teaching and learning.

I used this book as the requited text for my course on integrating play into mathematics learning within the program of graduate certificate in educational studies during the winter term of this year. The majority of my students were in-service mathematics teachers. Therefore, during the course learning time, my students had a chance of experiencing play in their mathematics teaching and sharing their experiences with their colleagues.

Su’s book profoundly impacted my course on integrating play into mathematics learning. Here’s how: a) recognizing the learning potential of play: Su’s book underscores the idea that incorporating play into mathematics education isn’t merely about fun; it’s about tapping into the profound learning potential inherent in playful interactions. By embracing this perspective, my course emphasized the importance of playful practices as avenues for deeper understanding and appreciation of mathematical concepts and thinking; b) validating play as learning: Su’s work advocates for understanding play as a legitimate form of learning across all ages. This aligns with my course’s goal of integrating play into mathematics learning for all learners, highlighting that playful exploration fosters critical thinking, problem-solving skills, and creativity. By leveraging games, puzzles, and hands-on activities, students can engage with mathematical concepts in meaningful ways; c) empowering educators in task selection: Su’s insights can empower educators to critically select tasks, contexts, and materials that encourage playful engagement with mathematics. My course emphasized the importance of creating environments where mathematical exploration was encouraged, mistakes were embraced as learning opportunities, and students felt empowered to shape their mathematical journey; d) cultivating a culture of mathematical play: Su’s book guided me in fostering a culture of mathematical play within my classroom. By embracing mathematics through playful learning, my course enhanced my students’ understanding of mathematics teaching and learning and cultivated a deeper appreciation for mathematics within their teaching practice and professional learning communities; e) embracing mathematics through play: Su’s perspective encourages viewing mathematics through the lens of play, appreciating its beauty, permanence, truth, and power. My course emphasized embracing the inherent struggles in mathematical exploration and the importance of justice and freedom in mathematical pursuits. By fostering a love for mathematics through playful engagement, my course contributed to vibrant mathematical communities where curiosity thrives, and learning knows no bounds.

 

 

Previous Good Reads Mentioned

2023

♦ Introduction to the Theory of Optimization in Euclidean Space by Samia Challal

Recommended by Samia Challal (York University – Glendon Campus)

The book provides students with a robust background in Optimization. It is a self-contained resource for the instructor and for the student. The main theoretical theorems are provided with detailed proofs and followed with examples for illustrations. At the end of each section, some questions are suggested with complete solutions. Depending on the students’ mathematics background, one can skip the detailed proofs and direct the students’ attention to:

• • • focus on the intuitive ideas,
    • practice into acquiring the new strategies needed through solving optimization problems, and
    • discover different applications where optimization is involved.

 

♦ In pursuit of zeta–3: the world’s most mysterious unsolved math problem by Paul J. Nahin

Recommended by Tim Sibbald (Nipissing University)

This book is well suited to enrichment or encouragement for students who are interested in the field of mathematics. It is suitable for undergraduate students and somewhat accessible at the grade 12 level. The strength of the book is that it surveys many results from the rich topic of Riemann’s zeta function while being respectful for, but not bogged down by, rigour. It steers clear of the Riemann Hypothesis and focuses on the mysterious value of the zeta function at three. The value is known to be irrational, but an exact value is not known in spite of evidence suggesting it is likely to be a rational multiple of pi cubed. Within this milieu many results are discussed relating to the zeta function, gamma function, and Euler sums that arise naturally from the overall focus. The coverage of the book is well suited to undergraduate students because of the mix of infinite sums, integrals, products, and Fourier series—yet all topics are addressed in an accessible manner.

Personally, I visited many of the topics in this book when I was in grade 13. That shows my age, but also speaks to how one does not need a fully developed sense of calculus to enjoy the book. I recall being challenged by a variety of the concepts I found in the book in a good way. Revisiting the topic through this book pointed to some aspects that are new to me and serve as provocation to investigate recent findings.

 

♦ Aesthetics of Interdisciplinarity: Art and Mathematics by the editors Kristóf Fenyvesi and Tuuli Lähdesmäki

Recommended by Amenda Chow (York University)

This book dives into the interplay between art and mathematics by showcasing a wide-ranging collection of articles written by various experts. Many of the articles include a selection of thoughtful, complementary, and artistic figures. Some topics discussed are:

• • geometry of India’s ancient temple cave art;
  • drawings containing a hidden image (known as anamorphosis drawings);
  • mathematical modelling influencing scientific discoveries like DNA and viruses;
  • African weaving patterns in mats and baskets;
  • designs with optical effects and visual illusions; and
  • meaning and societal impact of geometry-based monuments.

There is much more in the book, and to begin, the first chapter is a discussion about the aesthetics of interdisciplinarity, which is a term created by the editors of the book to refer to the broad and deep relationship between art, mathematics, science, and technology. This introductory section also includes an overview of the global community that has evolved around the common enthusiasm and intrigue for the aesthetics of interdisciplinarity. Lastly, just a small note: overall, the focus of the book is on the art, with mathematics as a well-placed backdrop.

Why I liked the book?  I was introduced to ideas, connections, people, and art pieces that make me now see the world differently. For this I am grateful, and quite inspired. I feel more prepared to teach my upcoming first-year calculus course and my introduction to proofs course because it has given me insights on how to inspire my students’ learning. Many of the ideas and images in the book mesmerized me, and in the middle of reading it, I also felt happily nostalgic and tried out my spiragraph set after a nearly thirty-year long absence. As I child, I remember finding these spiragraph designs to be beautiful and hypnotizing, but at the time, I didn’t realize the underlying mathematical principles. Now I am in awe realizing math and art were part of my life from a young age. Above are some examples of sketches using a spiragraph.

Thank you to Professor Eva Knoll from Université du Québec à Montréal for suggesting I read this book.

 

♦ Inclusive Teaching by Kelly A. Hogan and Viji Sathy

Recommended by Zack Wolske (University of Toronto)

This book is based on their work towards a more inclusive environment using high-structure, flipped classes to teach introduction to biology and statistics at a large research university with limited institutional support and free rein to decide how to teach.

If you are looking to make incremental changes to teach more inclusively; if you would ask “who might be left behind, and how can we invite them in?” about your teaching; if you are reflecting and looking for questions; if you seek data and transparency with students, TAs, and faculty about your practices; if you want to see specific examples of syllabi, interactions in and out of the classroom, and instructor checklists for high structure courses; if the authors’ situation resonates with you; check out this book.

You can find examples and book club prompts at inclusifiED.com, and hear the authors discuss the book on the Teaching in Higher Ed podcast, episode 425 (and 365, 272, or 197 for some overlapping work).

 

Also recommended by Rachael A. Lewitzky (George Brown College) & Asia Majeed (University of Toronto)

This book explores teaching strategies the authors use to foster a sense of inclusion in their college classrooms. Two questions guide the authors’ approach to fostering an inclusive environment: 1) Who might be left behind as a result of my practice? 2) How can I invite those students in? The book provides insight about how each author’s teaching practice has evolved – the challenges they have faced and the successes they have experienced. Topics include course structure, class design and facilitation, inclusive practices within and beyond the classroom, as well as reflection on teaching practices.

As introductory science, technology, engineering, and math (STEM) course instructors, they explain the challenges of feeling the need to include an abundance of content in a limited amount of time. They highlight the value of identifying the skills and outcomes of a course and working backwards to determine what content, ideas, and concepts to include in the course. The authors describe what their courses look like from start to finish. From how they structure their course syllabi and activities they complete at the beginning of the term (e.g., opportunities for student-instructor and student-student interactions; creating conditions where it is safe to make mistakes; presenting societal and personal relevance in course) to structured small group and large group discussions, to demystifying the purpose of office hours, the authors provide suggestions and strategies.

The personable way in which this book is written makes it feel like sitting down with a friend and talking about how to learn and grow as an educator. We enjoyed reading this book and sharing our thoughts with one another about how we could employ some approaches discussed in the book. Inclusive Teaching provides readers with the chance to reflect on their own teaching philosophy and highlights opportunities for creating a more inclusive learning environment.

 

2022

♦ Making a grade: Victorian examinations and the rise of standardized testing by James Elwick

Recommended by Tim Sibbald (Associate Professor, Schulich School of Education, Nipissing University)

♦ Shape by Jordan Ellenberg

Recommended by Sean Fitzpatrick (Instructor III, University of Lethbridge)

Superficially, Shape is a book about geometry. It is not a book from which one can learn geometry. However, it is more of a love letter to the subject, and a description of the many ways in which it is woven throughout our daily lives. Recurring themes include the structure of games, and mathematical modelling in biology, including the spread of infectious diseases. Ellenberg does a great job of keeping things entertaining using historical perspective and stories of the personalities involved.

The book ends with a fascinating chapter on the efforts by both mathematicians and politicians to tackle partisan gerrymandering, and describe precisely what would make an electoral map fair. It is a great look under the hood at the process of mathematical thinking.

The book is written with the non-expert in mind, but anyone teaching undergraduate mathematics is sure to find a nugget or two they can use in their classrooms.

 

♦ The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math by Steven Strogatz

Recommended by Julie Plante (CEGEP Instructor, Vanier College)

A teacher and his student will stay in touch for over 30 years, always united by their love of Calculus, discussing mathematical problems, their lives, everything … Very touching. A must read for any Math teacher…

 

♦ How Not to be Wrong by Steven Strogatz

Recommended by Wes Maciejewski (Red Deer Polytechnic)

I went to the bookstore to buy Shape (see Sean Fitzpatrick’s review) by Ellenberg and this, his first, sat next to it. I picked up both. I wanted Shape because I’ve been on this kick lately, thinking about how topology and contemporary notions of “shape” might be infused in K-12, and lower-level university, education. Turns out, How Not to be Wrong is the book I needed to read. Why should I be bothered about curriculum? Really: it’s a desire to tell better, more interesting, more relevant stories. How Not to be Wrong does that; it’s the finest example of mathematical storytelling. Stories I, and perhaps you, haven’t heard.

Ellenberg narrates in 5 themes: Linearity, Inference, Expectation, Regression, Existence. Each is a winding path through mathematics used and abused, often wrongly, and often to mislead, intentionally or haphazardly. He brings together wild stories of dead fish, decoding the Torah, the poor economics of the Laffer curve, and voting (among others) and deftly brings forth the underlying mathematics: people think too much and too often in terms of lines; we’d like to use mathematics as a crystal ball when it isn’t; probability and expectation remain hard to comprehend; we search for causes when there might not be any; and consensus is not so easy to discern. Ellenberg is to math as James Burke is to the history of science and technology: he makes connections and guides us to rethink what we take as known. He does this through his own brand of engaging narration.

Going back to how this might be relevant to you, the educator. If we ever only read the same, yellowed texts, we squeeze them dry of all their inspiration. Our stories – the heart of good teaching – become impotent. Read better stories to tell better stories. Read How Not to be Wrong. Make math interesting again.

 

♦ The Housekeeper and the Professor by Yōko Ogawa

Recommended by Julie Plante (CEGEP Instructor, Vanier College)

A wonderful novel written about Mathematics as much as mathematicians… The novel is very appreciated by non-mathematicians as well as mathematicians. A female house-keeper is introduced to basic number theory by an old professor. The beauty of pure Mathematics is extraordinarily put in words in this writing.

 

♦ Things to Make and Do in the Fourth Dimension: A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More by Matt Parker

Recommended by Asia Matthew (Mathematics Tutor, Quest University)

See Asia’s Review in the March Issue of Crux:

https://cms.math.ca/publications/crux/issue/?volume=48&issue=3

 

♦ Mathematics for Human Flourishing by Francis Su

Recommended by Sean Fitzpatrick (Instructor III, University of Lethbridge)

This is a book about mathematics, and leading a fulfilling human existence, and how the former helps with the latter. Su examines the role of mathematics in our lives through the lens of a series of human virtues, including exploration, play, truth, beauty, struggle, and justice. A unique feature of the book is the inclusion of some of Su’s correspondence with Christopher Jackson, an inmate in a US federal penitentiary, who wants to become a mathematician. The book is a rewarding read for both mathematicians and the math-averse. It is an excellent choice for an assigned reading in any class containing math-anxious students. The end of the book contains a collection of prompts for reading responses, with further prompts and other resources available on Su’s website.