Mathematical Toolbox

I recently completed my master’s research on the use of instructional videos. One of the issues that came up in my results and conclusions was the issue of retention. After teaching my Tier III mathematics students, they took post-tests which they all passed. However when I gave them summative assessment covering all the topics at the end of the study, not all students did well. There was an overall decrease in scores, but for some students it was more dramatic than others.

Two students in particular remembered almost nothing. This was very concerning as they had already spent two months receiving interventions! I thought about it and came to the conclusion that the topics needed to be revisited frequently throughout the year even after the student had finished and become proficient with the topic.


I found in my closet a baby wipes box that had been left behind by another teacher. I wrapped in shiny silver wrapping paper then attached labels: “Mathematical Toolbox”. Inside I put two different types of cards: The yellow orange cards were to be used for skills and the orange cards were to be used for vocabulary.



I began using it with one student, starting from the first topic we ever covered, creating vocabulary and skill cards for mixed numbers and improper fractions. Then we worked on practice problems for turning mixed numbers into improper fractions and vice versa. The first day that is as far as we got. The second day, we reviewed the vocabulary and differentiated between them: How were they similar, How were they different? Then we differentiated between the two skills. The student solved practice problems for each. Then we moved to a new topic, prime factorization as the skill, prime number and composite number as the vocabulary.

The goal wasn’t to master the topic before moving on to the next topic. The goal was to provide the student with review and opportunities to practice over a long period of time. By this time, I have met with this student five times, each time practicing skills already in the box, and adding new skills and vocabulary. The student identifies and differentiates between the vocabulary and skills, and solves problems, faster each time.

My previous method was to provide a pretest, teaching the lesson, provide a post test, then move on and never specifically revisit the topic (a topic that came up naturally was prime factorization with finding the greatest common factors and the least common multiple. This was also the topic that had the highest score on the post-assessment).

The initial process of pre-test, lesson, post-test worked, but in a Tier III intervention setting it is necessary that the topics are revisited, reviewed, and reemphasized. It also comes down to providing the students with repeated and extensive opportunities for independent practice. Students need to have many opportunities over time to practice the skills on their own to have a true long lasting mastery of the content.


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