Q: Let's start with some background information. Where do you teach, what grade level, and for how long?
A: I've been teaching for eleven years. I taught 4th grade for 8 years, 3rd and 4th grade math for one year, and 5th grade for 2 years. I teach in Haverhill, MA.
Q: What prompted you to write this book?
A: Teaching math at the third-, fourth-, and fifth-grade levels, I've noticed and taken an interest in how children learn the basic math facts. This prompted me to conduct an action research project to study approaches to teaching math facts. From my research, I concluded that students learn and retain automaticity of facts when they are taught the facts in a meaningful way using strategies and looking for patterns. Providing opportunities for meaningful practice is another important piece.
Q: There are a lot of books out there that attempt to teach the multiplication facts. How is yours different?
A: Over the years, I've shopped at teacher stores, bookstores, and online looking for books that teach multiplication facts in this manner. I have yet to find any! Most of the books on the market simply provide worksheets with the facts repeated several times--or speed tests. I bought and tried many of these books with my students and found that most of them didn't work.
When I conducted my action research, I started making my own practice pages on the computer, and that led to Multiplication Success with Algebra. The approach I use in this book is different because students have to stop and think before they answer. Also, the practice pages encourage algebraic thinking.
Q: So, in more detail, how does your approach work?
A: The activities in my book are designed to provide students with meaningful practice as they learn the multiplication facts. It's a lot different from the "drill and kill" approach.
For example:
- Students use the Identity Property to figure out that any number multiplied by 1 is equal to the number (n x 1 = n) and the Zero Product Property, which states that any number multiplied by zero is always equal to zero (n x 0 = 0).
- Students use the doubling/halving strategy to help them learn many of the multiplication facts. For example, if you multiply a number by 2 and then double it, you will get the answer to multiplying a number by 4. If you multiply a number by 4 and cut it in half, you will get the answer to multiplying a number by 2.
n x 2 x 2 = n x 4
(n x 4) / 2 = n x 2
- Students are also prompted to look for patterns to help them figure out the products. For example, all numbers multiplied by 9 have a digit sum of 9; all numbers multiplied by 5 will have a 0 or 5 in the ones place.
Q: Can you explain why you included "algebra" in the title? What do multiplication and algebra have to do with each other?
A: Well, patterns are a big part of early algebra learning, aren't they? And while students are learning the multiplication facts using strategies and looking for patterns, they are also practicing algebraic ideas like balance, variable, and function.
For example:
- Balance involves the idea that the equal sign shows the relationship between numbers. So as students are practicing the 10 and 5 multiplication tables, they are also practicing balance when they solve the equation:
4 x 5 = r x 10
r = _____
- Variables are the unknowns in the equation, and this book provides students with practice in determining the value of the variable in the equation. For example, in the equation A x 3 = 15, the student solves for A, the unknown.
- Function is another idea that students practice. Students use the given rule to determine the output in a function table.
Let's face it, the curriculum can be overwhelming and difficult to fit into the school day, so an approach that synthesizes multiplication and algebra concepts has an important advantage.
Q: How would you recommend that teachers use this book?
A: Well, it's all spelled out in the introduction to the book, but basically I recommend that students take 10-15 minutes to independently complete one practice sheet per day, Monday through Thursday. They can do this sometime during math class or as homework the night before. After they have completed the day's practice sheet, they then correct their worksheets together as a class. On Friday, they take a quiz focusing on that week's multiplication fact. All practice sheets and quizzes are provided in the book, but I certainly invite teachers to take the approach and run with it.
Q: Can you say a little about how the activities in the book meet the Common Core State Standards?
A: The activities in the book basically meet the Operations and Algebraic Thinking standards for grades 3 and 4. They also meet some of the place value standards. There's a comprehensive chart in the Introduction that gives more details.
Q: Presumably, other teachers in your school have tried the approach. What kind of feedback have you gotten?
A: My colleague Jean and I use this approach, and we have seen positive results. Another colleague of mine began using the program and she loves it.
Q: Your colleagues must be excited to have the book to work with now.
A: Yes, many have asked me about it.
Q: Have you workshopped your ideas to a wider audience? Or do you plan to?
A: Honestly, I haven't thought about conducting workshops, but I am interested!
Q: Are you planning another book?
A: Yes, I have a draft of "Division Success with Algebra" almost ready to go!
Q: Anything else you'd like to add?
A: Just that I hope teachers will find this approach both sensible and feasible, and that they'll come back to these activities again and again, as I did. It's exciting to watch students gain confidence and fluency in using the multiplication facts, and I'm happy to have made a contribution to that process.
