**Concept-Based Curriculum and Instruction **

**Concept-Based Mathematics**

Jennifer Chang-Wathall

**Reviews For Concept-Based Mathematics**

This book is cutting edge. It is the next step to bring mathematics education into the 21st century. It needs to be in the hand

of every secondary mathematics teacher and teacher educator. All students deserve to experience the wonder and

passion for mathematics that Jennifer so obviously feels. It is time to change the age-old lament to empowering testimonials—

“I love mathematics!” “I can use mathematics every day to think and create!” “Math is fun!” “I get math!” **Dr. H. Lynn Erickson **

**Concept-Based Curriculum and Instruction for the Thinking Classroom**

"Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of

Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual

understandings. This book ignites the mathematical mind!"**Dr. Lois A. Lanning. AuthorDesigning Concept-based Curriculum for English-Language Arts, K-12**

"Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it's a boon to any educator who wants to bring math to life for students the world over."**Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant**

"Secondary teachers are constantly being encouraged to change their practice but few books have addressed the topics of secondary mathematics nor given examples that secondary teachers can relate to. This book does that. Another strength is the connection of the content to the math processes and practices, the heart of good instruction. The figures provided to summarize big ideas are excellent. I love the potential of this book for using it as a text for middle and secondary teachers, a guide for professional development, and a place for individual reflection. I know for sure that I would use it for my student teacher seminar class and anytime that I was instructing upper level math teachers. I’ve been waiting for this!”**Barbara Fox, Adjunct Professor, Student Teacher SupervisorUniversity of Massachusetts, Lesley University, Regis College**

“The author provides a solid rationale, backed up by numerous practical and authentic examples to increase the quality of conceptual math classroom teaching practices so needed to develop the next generation learners. This is a must have for any secondary school’s professional library.”**Dave Nagel, Author ConsultantCorwin / NZJ Learning (LLC)**

“One of the major strengths of the book is the examples and the visual diagrams that outline major topics. The book provides rubrics that allow teachers to determine where they are in their methodology and a opportunity to decide where they can improve their teaching strategies.”**Amanda McKee, High School Mathematics InstructorFlorence County School District #5**

“The major strength of the book is that it addresses teaching mathematics in a way that invites students to learn and encourages not only content knowledge, but depth of knowledge, rigour, and critical thinking. Inquiry is a means of synergizing your classroom and drawing students in so that they want to learn. This is going to require a change of mindset for teachers and the administrators alike as well as training. This book provides an opportunity for both.

This is an interesting and definitely new topic. I do believe that it is time for a change in the way in which mathematics is taught. Math is being taught the same old way that it has been taught for hundreds of years. It seems that Mathematicians are much more resistive to change than are other content areas as far as instructional methods are concerned. Inquiry is a method that has been around at least since the middle 1970’s, and has been used as an instructional method in some form or fashion since then. Students loved it then and love it now that it is making a resurgence in classrooms today. It is an effective method for teaching in that, when used correctly, student retention of information is great and understanding of material is much greater than in the regular classroom. This is thought to be due to the fact that students are using so many different means of input to get their message in to the brain. With Concept-Based Math they are using Visual, Auditory, Kinesthetic, Tactile, Work Individually, Work in Groups, Work Whole Group, Critical Thinking, and students are expected to stretch their minds further than possibly they have ever been expected to stretch them before. It is tough to do something new, to be a trailblazer, and this book is certainly doing that. I have never seen someone step outside the expected norms of instructional expectations in math, but this author does! She is kind of like the Galileo of Math instruction."**Pamela L. Opel, Intervention SpecialistGulfport School District**

"Jennie Wathall’s book offers a clear understanding of how complex learning of mathematics is, and how to use this understanding to create a thinking classroom. She explains, from a scientific point of view and in a very well-researched and comprehensive manner, sprinkled with plenty of practical examples, what is the interdependence between the processes and knowledge and how to plan, run and assess for a concept-based mathematics classroom. This book is a must-read for all mathematics educators, a book that should definitely be on the table in each mathematics office."**Dr. Daniela Vasile, Head of MathematicsSouth Island School, Hong Kong**

"Concept-Based Mathematics is a breakthrough which is needed in the 21st Century mathematical education worldwide. Designing Concept-Based Mathematics Curriculum provides a roadmap to overturn the old paradigm of direct instruction and replaces it with a post-20th Century guideline for what can make’s math education work."

**Mathematics Instructor, Curriculum DesignerThe Education Center, Aurora, CO **

"This book is a much needed topic! There is a need for a content-specific book on designing concept-based curriculum. The examples are not over generalized and can be adapted and modified for mathematics teachers interested in developing concept-based curriculum. I teach a summer graduate course on Curriculum and Instruction that uses Erickson’s book. Most of my students are mathematics teachers. If/when the book is published, I will give my students the option to purchase this book."

**Jamalee Stone**

**Associate Professor of Mathematics EducationBlack Hills State UniversitySpearfish, SD **

"The book explores issues in mathematics education which are quite contemporary. There is a need to move mathematics teachers away from traditional didactic approaches towards a more concept based approach and this book meets that need.

One of the strengths of this book is that it gives plenty of concrete examples to illustrate the processes that it advocates. Often one reads books like this that advocate particular approaches to teaching but they are highly theoretical and difficult to access. This book is easy to read and understand the concepts that the Author is trying to get across. I am not aware of any texts that address this specific topic in Mathematics in this way."

**Paul Chillingworth**

**Mathematics AdvisorMaths in Education and IndustryTrowbridge, Wiltshire, UK**

**This book is a great reference for all Mathematics Teachers. The author Jennifer Wathall is an expert in this field. The layout is easy to follow and the examples detailed enough to guide you through the process. This book is a concise and easy guide to understanding concept based teaching in Mathematics. All schools should be striving for a concept based curriculum, but if you are an MYP school or you follow the CCSS then buy a copy of this book now for your teachers.**

Peter McCombe

Head of Mathematics, DP Consultant

**This is an interesting and balance between theory and practice. Many educational books are very general and discuss goals, aims and philosophies in fairly abstract terms. Often Maths books, on the other hand, have lots of examples but very little of the theory behind them. Jennie’s book has roughly equal parts of both.**

The theoretical background of all of this comes from Lynn Erickson’s work on concept based learning. Lynn writes the foreword and the whole project has been supported by Lynn and Lois Lanning. This is where the book starts with definitions of the terms addressing the question of what we mean by concept based learning in Mathematics. There are the usual diagrams of Erickson and Lanning but annotated by Maths examples. Then we get the first key idea which is that inquiry led learning supports a deeper understanding of the concepts. Readers of Mathsthoughts.com will love this. Once we have that then it all flows from there. Jennie maintains there are different levels of inquiry and gives mathematical examples of activities at different levels,

Chapters often have intriguing questions as their titles. What are generalisations in Mathematics? What does a concept based classroom look like? How do I captivate students? The eight strategies for engaging the hearts and minds of students are offered as an answer to the last question. Every time a suggestion is put forward, it is accompanied by real examples of activities to set students, and ways to deliver them.

It is a book that is mathematical in its structure and style as well as its content. Jennie writes in a logical way, the prose is straightforward and well put together. Altogether it is an excellent synopsis of some really good practice in teaching Maths, underpinned by solid theory and demonstrated by useful examples. A great book for any Maths teacher.

Chris Binge

**Educator and Principal******

**www.educhanges.com www.mathsthoughts.com **

****I enjoyed reading this book very much. It is very rich and resourceful and will be a good reference for my PGDE and MEd students. It helps us make sense of various elements in our math pedagogy that may be described in different ways, like the comparison of mathematical processes described in different curricula. Through this book, I understand more about the theory from Lynn Erickson and can learn from rich examples of unit planning in IB.

**Lecturer**

**Faculty of Education **

**University of Hong Kong**

Teaching for deep understanding should be an aim for us all. In her book Jennifer provides advice for teachers to enable them to assist students to learn through interaction, investigation, confidence and enjoyment, while describing the important role of inquiry, discovery and verification. She describes methods of assessment through open inquiry tasks and open-ended questions. Jennifer affirms, with reference to current research, that such tasks help to make students independent and lifelong learners. There is a valuable summary at the end of every chapter and a list of summary questions which are an extremely valuable aspect of her book. It would be feasible for mathematics faculties in schools to focus regularly on these for valuable discussion and reflection for all mathematics staff. Jennifer also provides valuable templates for teacher use and includes examples of the effective integration of technology in the mathematics classroom, making the vital point that, ‘it’s not *what* you use it’s *how* you use it.’ One of her most valuable chapters addresses commonly heard concerns and misconceptions about a concept-based curriculum. In short, a gem for the library of any mathematics faculty genuinely focused on teaching mathematics in today’s modern world.**Robyn Gregory, MSc (Mathematics), Dip. EdMathematics Teacher, Australian International School Hong Kong**

“Jennifer Wathall’s book is a well-researched resource that coherently explains the theory of Concept-based Mathematics and how to put it into practice using distinct steps. Expert guidance is given with curriculum writing, teaching and learning and assessing. Across all of these different aspects, Wathall comprehensively supports educators with multiple, practical examples and by encouraging interaction and reflection throughout the book. Although Wathall’s book was written for a Secondary school audience, the frameworks she uses is also an invaluable resource for Primary mathematics specialists and elementary generalists. The complementary resources available online, provides digital access to key figures, modules and planning templates. Any educator who is striving to teach Mathematics using inductive, inquiry-based methods and who is interested in taking the complexity out of Concept-based Mathematics should have a copy of this book. Nothing else out there empowers teachers with skills and strategies to implement Concept-based Mathematics better, except a workshop with Jennifer Wathall herself! I am looking forward to putting what I have learned from this book into practice in the classroom.”**Angeline AowPYP Workshop Leader and Concept-based Curriculum and Instruction Presenter/Trainer**

As an Early Years teacher I admit that I was initially a bit hesitant to read Jennifer Wathall’s book, Concept Based Mathematics, as I thought it might not be relevant or applicable to the Early Years curriculum, but now I can say I’m so glad that I did. Jennifer is nothing short of a math guru and this book is a fantastic resource for any teacher who wants to make their math lessons more inductive and inquiry based. This book takes you with ease through the process of planning, teaching and assessing concept-based mathematics. While many of the examples in the book are from secondary lessons, the principles that she teaches, and the clarity with which she explains them, are applicable at all grade levels, including the Early Years. I would highly recommend this book if you are interested in developing a deeper understanding of concept-based learning in your math lessons.

Pamela Ostler

Early Years Educator and Concept-Based Curriculum and Instruction Presenter

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