Struggles with Static Math Examples

A recent article from Education Week highlighted a research project conducted by the National Research and Development Center on Cognition and Mathematics Instruction that is testing how to make paper-based textbooks more effective for students. Researchers are examining the effectiveness of “better text and illustration integration, use of sample problems, and homework and practice pacing”. One of the preliminary findings from the study caught my eye and resonated with my past classroom experience with paper-based textbooks: Researchers observed that middle school students, when working through sections that provided a sample problem for guidance, often neglected to read the sample problem and did not use it to form a problem solving strategy.

I am sure every teacher has observed this at some point in his or her career. Students observe pages of example problems at the beginning of a section, skip them, look to the board to discover what problems are in the homework set, and begin working on them (often before the teacher is finished with instruction). I remember preparing for an upcoming textbook adoption a few years ago. I had quite the assortment of sample textbooks spread out along my back counter to review. I asked my students which of the sample texts they would prefer. Their answer was profound: “The book that is the least cluttered.” I began to realize that static examples with step-by-step text explanations crammed to the side were intimidating to my students.


Again, this is where digital texts are offering a creative alternative. Discovery Education’s Math Techbook’s inquiry-based approach presents new content that is not static, but rather inquisitive and interactive in nature, removing the need for static sample problems during initial instruction. Some lessons feature videos to stimulate thought, some utilize Technology Enhanced Items to piece together prior knowledge to uncover new concepts, while others immerse students in a digital interactive they can explore. My students are more engaged when they encounter content that is relevant, realistic, and interactive.

Not only is the instructional content of Math Techbook interactive, but many of the practice problems are as well. After navigating through a lesson, students are presented with two sections for practice problems- Coach and Play. Coach problems, as the name implies, actually offer feedback to students as they work with new concepts. Students see feedback messages when they choose incorrect answers, prompting them to examine the misconceptions that prompted their choices. Students also see feedback if they choose the correct answer(s), allowing instant feedback rather than turning to the back of the book to search for answers to odd-numbered questions. Coach problems allow for “guided” practice to take place at the pace of the student.

The Play section allows students to practice concepts in a competitive atmosphere. Students have the opportunity to earn up to three badges (signifying one to three stars) per concept, one for every five problems they answer correctly. As students earn badges, they accumulate on a rewards screen, showing students their progress as they advance through the curriculum. The gasification element of the Play section fosters greater engagement with students as they look to continually advance to badges with greater numbers of stars.

In the end, I’m sure that the research project will help improve the quality of paper-based books. But I don’t think the improvements will solve the basic problems they present teachers and students. Teachers need curriculum that is engaging, interactive, and captures students’ interest. They also need to make timely, data-based decisions that impact the quality of their instruction/remediation real-time, not the following school year.  The digital medium is beginning to offer creative solutions that make that dream a reality.




  1. entrepreneur trainer said:

    It would seem this problem should be self-correcting. Once the students find out that departing from the instructions is counterproductive (poor scores, takes longer), they will adapt their behavior accordingly. Especially if the instructor points this out beforehand — and afterward.

    Once when taking the SAT Verbal test, I tried a strategy of looking at the questions before reading the article — thinking it would be faster to scan the article for terms used in the questions. We’ll, it didn’t turn out that way. Lesson learned.

  2. MEPCO said:

    Thank you for an good article so well written. So informative and insightful.
    I found the best site to learn basic mathematics thru dynamic worksheets is
    I hope it will be very useful for your kids to practice and learn math easily.

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