Do you feel stressed about covering your entire math textbook this school year? How should we view textbooks? Are they our masters demanding every section and problem be covered?
Textbooks are wonderful tools to provide content, learning activities, and homework problems. However, we often feel duty-bound to “cover” all of the textbook material. Certainly, districts and departments make decisions about what chapters should be covered, but that still leaves a lot of grey area in terms of coverage.
It’s important to consider what students already know, and what is most important for them to learn in the long run. From there, we can set out our priorities for the chapters and the order we will cover them. Within the chapters, we make similar decisions about the sections.
Next, we view the individual lessons including the text, learning activities, and homework problems. Some textbooks provide a central interactive task that allow teachers and parents to help students make sense of the mathematics. (See examples below.) Other textbooks provide steps for the easy exercises but leave the problem solving for the end of the homework. In this case, I often will choose a few of the more interesting story problems and build my lesson from them so that there are good contexts for the children to connect to. You still incorporate the basics, but from a standpoint of making meaning out of the mathematics. Another way around a weak curriculum is to present tasks from a stronger curriculum, and then assign more familiar homework..
If you prefer easing into problem solving on a weekly basis, the Illuminations website hosts great tasks, applets, questions, and answer keys free for the taking. You can search by grade band or math topic. I have used it often, and I highly recommend it. See https://illuminations.nctm.org/
When assigning homework, 6 or 8 exercises to reinforce the concepts is sufficient. Alternatively, a couple of more in-depth tasks with several parts would be enough. The objective is to deepen understanding and build skill while avoiding busy work. Families can modify assignments as needed to provide flexibility for students needing extension or remediation.
As the school year progresses, there may be home or school activities that lend themselves to mathematical thinking. Capture these moments, and allow them to “count” for certain sections of your math curriculum, buying you some time as well. For example, a school fundraiser would be a context for reinforcing decimal operations as students set goals and keep track of money earned.
In sum, textbooks used as tools aid the teaching and learning process. Textbooks should not be viewed as tyrants demanding “coverage”.
Suggested task-oriented math curriculum is below. Using older versions tends to be a lot cheaper on Amazon but are still quality curriculum. The Math for Adults Foundation’s Math Library, located at 2000 W McIntosh Rd, Griffin GA, holds hundreds of curriculum units donated by the University of Georgia. The checkout period is 1-semester. If in the vicinity, contact Dr. Andrea Knapp: aknapp@mapsfoundation.com, 309-287-2373.
Connected Math Project (middle school) https://connectedmath.msu.edu/
Math Expressions (elementary)
Investigations in Number, Data, & Space (elementary)
Everyday Math (elementary)
ThinkMath (elementary)