  # Interleaving and Spacing Math in Second Grade • Category:
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In elementary education within a public-school setting teachers are expected to use commercial math materials to teach grade level content. However, many of these commercial materials lack the appropriate cognitive learning strategies to help students learn and retain the inforamtion. There are a number of textbooks related to math content that use blocking or mixed review strategies to help students learn the content. Blocked practice is when students are given problems to solve where they are required to use the same strategy over and over again (see Figure 1). Mixed review is an assignment given usually at the end of a unit where a variety of problems come from the lessons taught from that unit. Unfortunately, these methods do not help students with retrevial for the long term (Rohrer et al, 2014). When blocking and mixed method strategies are used, students are more likely to forget the information. Interleaving the content particularly in math, helps students retain the information for a longer period of time. Interleaving is when students are given problems that require them to use different strategies to solve them (Rohrer et al., 2017). Along with interleaving, spacing is an additional learning strategy where students remember more when information is spaced out(Fazio,2018).

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My district uses the commercial math textbook Ready Math. Ready Math is designed by chunking the four domains (Operations and Algebraic Thinking, Numbers and Operations in Base Ten, Measurement and Data, and Geometry) into units. Each unit has a certain amount of lessons and within each lesson a skill is taught that aligns with the domain and state standards. After each lesson there is a quiz which consists of blocked problems for assessment. At the end of the unit a unit practice is given which consists of mixed review problems from the current unit of study. There is also a performance task at the end of the unit that requires students to apply higher-order thinking skills to real world problem solving. Interleaving is not a learning strategy that Ready Math incorporates and there is virtually no spacing of the content. In Ready Math students only see a lesson one time and will not see it again in the textbook. When teachers begin to prepare students for state tests, usually in March or April, then they will review the content from previous lessons. That means that the content that was taught in August is not seen again until March or April. Students have a difficult time recalling this information because they have only been exposed to it one time and because a large amount of time had passed since they had to use this information. Since this program is mandated by my district, I would like to propose a solution as to how to incorporate interleaving and spacing while using the textbook curriculum.

Incorporating interleaved and spaced practice combined with the textbook curriculum will help students to recall information for the long term. At the beginning of every lesson a warm up will be used that is designed to interleave problems from the day(s) before. So for example, beginning with unit 1 after lesson 1 is taught and before lesson 2, a warm up will be given to include problems from lesson 1. Then after lesson 2 is taught, a warm up will be given to include interleaved problems from lessons 1 and 2 before lesson 3. Next, a warm up of interleaved problems from lessons 1, 2, and 3 will be given before lesson 4. After that, a warm up of interleaved problems of lessons 1, 2, 3, and 4 will be given before lesson 5.

Next, a warm up of interleaved problems from lessons 1, 2, 3, 4, and 5 will be given before lesson 6. Finally, a game like review (Jeopardy) of interleaved problems from the entire unit will be given on lessons before the unit assessment is given (see Figure 2). An addition of review of previous unit lessons with interleaved problems will be incorporated in the subsequent units (see Figure 3.) Since Unit 1 was the longest (15 lessons total) I decided to space the interleaved review for the middle and end of the unit. Taking into consideration that my students are 7 and 8 years old, I decided to space out the warm ups to everyday as opposed to every 5 days. This format will be followed for all of the subsequent units in the textbook. Finally, a cumulative review of interleaved problems consisting of all 3 units will be given at the end of unit 3.

## Justification for Solution

The effect size that spacing has on learning and retention is notable (Dempster, 1989, p. 310). Spacing out the retrevial practice of the unit reviews as well as review of lesson content will improve student recall and enhance memory retrevial for a longer period of time. In a study of foreign language word pairs, subjects were able to retrieve information in the long term due in part, to spacing of the tests (Bahrick, 1993). In another study, one group of students received blocked math problems and the other interleaved problems. When they were tested a week later, the students who received the interleaved problems did better than those with the blocked problems (Rohrer, Taylor,2007). Interleaving makes student decided on a strategy compared to blocked problems where students already know what strategy they will use to solve the problem.( Rohrer, Dedrick,& Agarwal, 2017).

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