Introduction
You would think that once you learn something, you'll never forget it, but that couldn't be further from the truth. You forget more the longer it has been since you learned the content. It is inevitable that you will "forget" the material if you never revisit it. The term used is "forget" because, everything you have ever seen or learned is stored in your memory; all you need is the appropriate stimulus to bring it back.
Making our remember a lot of information is hard to achieve. Briones (2016) compared reviewing in to walking over a path in the forest. When you first learn information, the path is all cleared and really easy to walk through. To recall the information, all you have to do is go down the path which will be quick since it is cleared. But say you don’t review the information at all, then the path starts to get overgrown with plants.
Following the analogy, Blocked and Interleaved Reviews are both ways to clear the path in the forest however, the difference is the length of path being cleared to go back from the start of trail. Blocked reviews clear only the closest path and leave the rest while interleaved reviews clears the whole trail (from the start to end) to make sure that a person can go back in any part of the trail if needed. However, in the study of Mariano (2024), both of them were proven effective in improving student performance.
This analogy arrays Mayfield and Chase (2002) findings that during review sessions, students primarily engaged in two types of practice: (a) blocked practice, where they practiced the rule from the previous session, or (b) interleaved practice, where they practiced the rule from the previous session along with rules from even earlier sessions.
To make sure the success of the reviews, the teacher must plan and understand basic rudiments of interleaved practice to apply in your reviews as an alternative or support to blocked traditional reviews:
Planning
Students might experience a drop in their academic performance over the summer, especially in subjects like mathematics. Students who don't practice math over the summer may find it difficult to stay up with new content when they return to school because math is a subject where new knowledge builds on what has already been taught. This may cause them to feel discouraged since they believe their math skills have declined. For this reason, it's critical to address the summer slide and stop the math skill loss (Austrew, 2022). Because of this, it is important to plan to scaffold the students in reaching the skills that have declined during the summer break that is needed in your future discussion in Math class.
One of the productive ways to start the school year is to do a diagnostic test. A typical diagnostic test covers the topics to be learned to measure students capability or to assess advanced students. However it will be more beneficial to include pre-requisite skills that might be needed along the way in the course. For example, transformation and square root topics may require the skill of integers which they might know in the previous grade but forgotten because of the summer break. The results of the diagnostic test will give a picture, not only of those who are advanced but also those who are in need of remediation and which pre-requisite skills you should include in your first interleaved review.
Aside from content, you should also plan your class structure. Implementing interleaved review is ideal for longer classes as it may take 10-15 minute to complete the routine of the review. In the study of Mariano (2024), the interleaved reviews were done in 55 minute classes with 3 example questions each day. It may take toll on your class instruction time but it will pay off eventually at end in the cumulative assessments.
The planning process involves adopting the second habit from Stephen Covey's "The 7 Habits of Highly Effective People," which emphasizes "beginning with the end in mind." This means having a clear destination to understand your current position and ensure your actions align with your goals. The studies on interleaved practice aim to prepare students for cumulative tests effectively. For instance, Mariano's 2024 study focused on helping students succeed in End-of-Grade Assessments in Mathematics. Before developing interleaved reviews, identify your specific goals, such as achievement tests or contests, and clarify expectations, scope, and potential topics that might challenge students. This clarification allows for aligning interleaved reviews with the targeted outcomes for better student success.
Bridging the gap and establishing interleaved review in class structure (as mentioned in paragraph 6 and 7) are the first walk towards interleaving the reviews but comprehensive plan is needed to make sure that you will end up in the right track. The table below is the Distribution of Standards in Interleaved Reviews used in Mariano (2024) study. Having the “end in mind” in the process of planning, the topics from 1st-3rd Quarters were included with 4th Quarter topics to guarantee that student will still recall all the skills needed for the EOG.
Figure 1 Distribution of Standards (Mariano, 2024)
Although there is no consistent pattern in the placement of standards in the example above, the teacher was very intentional in the placing standards in each day, not only to relate old concepts to the current topics but also based on the needs of the class that the teacher observed over time. In the beginning of school year setting, you can include in the Week 1 and 2 the pre-requisite skills that they need to master as you gradually include the latest topics being covered. As time progress, more and more topics will be introduced in the class and more topics need to be included the interleaved reviews that why it is necessary to create your planning ahead and plug them into a spreadsheet to make it easier to check if all topics are covered fairly or reasonably at the end of quarter, semester or year.
Creation
Rohrer et al. (2020) highlighted the prevalence of blocked practice in US middle school mathematics textbooks, underscoring the necessity for more interleaved practice problems. They argue that, given the substantial benefits of interleaved practice, textbooks should offer an adequate supply of such problems, as these resources are crucial for student learning. While teachers may create their own assignments or source materials online, these alternatives can be time-consuming and expensive. Consequently, the design and content of mathematics textbooks need to be evidence-based to effectively support student learning.
If the teacher is eager to implement the interleaved reviews, the teacher will go beyond the provided textbook in the classroom and create his/her own materials which add burden into his/her preparations. Rohrer et al. (2020) suggests that if the textbook, which is the primary resource in class, are already interleaved, it will be easier for the teacher and students to do interleave practice in class and can more focus on learning than the preparation. With instructional interventions that specifically support students in using comparison strategies tailored to the students’ abilities, the learning materials, and the learning objectives, interleaving could perform to its full potential for school learning.
The scarcity of interleaved textbooks are not only a concern in USA as well as in other countries too however there are only few to nothing available studies for this matter. However, to create the resources for your interleaved reviews, you need to combine the examples from different books based on the plan that you have made (as mentioned on the previous part). The attached below is the example of the interleaved review used in the study of Mariano (2024).
Figure 2 Sample Interleaved Review Sheet
In creating your questions for interleaved reviews, Mariano (2024) study suggests to create questions using the following tiers.
Tier 1: Skill-based questions - these questions are used in the early stage of interleaving reviews right after the lesson was covered. Focus on the direct mathematical equations or number sentence that the students need to solve.
Tier 2: Word Problems - these questions are used after the students achieved the Tier 1. Word problems apply skills learned in more realistic scenarios. This type of question improves reading ability as well as the mathematical sense of a student.
Tier 3: Multi-step questions - these questions are used after the students achieved the Tier 2. These questions (typically in word problems) require one or two steps of computation before actually solving for the target skill. These questions enhance critical thinking and reasoning skills.
Tier 4: Integrated to other concepts - these questions are used after students achieved Tier 3. These questions (typically in word problems) do not provide explicit method to get the final answer. The students need to integrate the things he/she have learned to get the correct answer. These questions make student visualize the problem and decide the best way of solving it. This is the highest form interleaving review. Dunlosky (2013) pointed that interleaved practice encourages students to first identify, recognize, and distinguish between various problem kinds or concepts before diving into problem solving.
Although the questions in the interleaved reviews are tiered, this is in the ideal situation. The highest tier of questioning in the interleaved reviews still rely on the topic being reviewed.
Execution
In the study of Mariano (2024), the ideal whole process of an interleaved review lasts for 10-15 minutes in a class per day. Again the term is “ideal” because the time may vary depending on your situation or time schedule. What matters most is that you will be able to follow the routine in the interleaved review:
Independent work/group work - After the class has settled and the interleaved reviews have been distributed, set a five (5) minute timer to allow the students to answer the questions of the day. At this point, try to give them as little assistance as possible. Walk around to see if everyone is doing their task and how they are answering the questions. The Captain-Co-Captain technique was employed in Mariano's (2024) study. The teacher is the "Captain," and each group will be assigned a "co-captain" (usually the most proficient math students) to ensure that all passengers (group members) are okay. During the 5-minute independent/group work, the co-captain will assist their passengers in solving the problem while guiding them to the correct solution. According to Keerthirathne (2020), peer learning benefits everyone. It enables students to share their knowledge, attitudes, and abilities with their peers. Peer learning works better when the learning objectives are clear. Because the learner participates in the learning teaching process throughout the learning experience, the learning environment is conducive to peer learning. The learner is not passive and unaccompanied. The learner manages his or her learning environment and considers how to learn. He or she participates in a learning activity with two or more others. The students get opportunity to teach and be taught by one another. Therefore, the learning environment is cooperative.
Presentation - After answering the questions for 5 minutes, ask a student to answer each problem. In the first few weeks, you need to model how they should present their answer. It is better if you have a document camera viewer so the class can see what you or your students are writing on the paper, but if that is not available, you can also make them answer on the board.
Provide feedback - Feedback is important if the class got the answer to the question correctly. however, make sure to provide a judgement-free environment to make the students feel that they will not be punished or embarrassed if they get the wrong answer. If the student or the whole class got the wrong answer, ask them what they did and help them to find out ways to correct their answer so they will not stumble on the same problem again, if they encounter it again next time.
After revealing the correct answer, make sure that the student understand how you solve for the correct answer. Make them change their wrong answer on their own paper. Note: the example interleaved review has only 4 days to give way for your quizzes on the 5th day.
Reflection
The success of interleaved reviews rely mostly on its consistency of usage in class. Remember that the premise behind the interleaved technique is that practice spread throughout many topics and time periods can promote deeper learning, better retention, and more effective knowledge transmission (Rohrer et al., 2016). To measure the success of execution, you must make some ways of reflection which can help you to decide whether to change your first plan of interleaving or it working enough to continue.
Do not depend solely on quiz/unit test results - quiz and unit test results won’t show you the impact of interleaving reviews. These evaluations are usually non-cumulative and focus solely on a particular lesson or chapter. Dunlosky et al. (2013) discovered in their study that students engaged in interleaved practice achieved lower scores on the practice test (88% vs 56%) but performed better on the final test (23% vs 64%). Mariano (2024) similarly noted that students who received blocked review achieved better quiz scores than those who had interleaved review in Volume (78.6% vs 64%) and Pythagorean / Distance (69.7% vs 57.3%), yet interleaved reviews outperformed in the posttest (68.48 vs. 50.29). Nonetheless, this section does not imply that you should refrain from taking quizzes and unit tests. These evaluations are equally vital for gauging student comprehension of the lesson or unit you have taught. In interleaved reviews, rather than overwhelming them with practice examples on the current subject, you incorporate topics previously studied that could influence their performance in the ongoing lesson. Ensure that your students understand that the quizzes and unit tests evaluate their comprehension of recent discussions as well as cumulative assessments covering the entire course, quarter, semester, or year.
Blocked reviews are also necessary - it was proven in Mariano (2024) study that blocked reviews can be as effective as interleaved reviews if it is done consistently and religiously. Integrated interleaved-blocked reviews will make sure that students will master current topics for the non-cumulative quizzes and unit tests while building strong foundations by consistently spacing former topics for cumulative assessments at the end of the quarter, semester or year.
Cumulative evaluations for feedback - evaluating students through cumulative assessments will allow you to understand the true status of their skills. This evaluation will provide valuable insights into your upcoming strategy, helping you determine whether to modify or proceed with your existing plan and decide on the tier of questioning to employ in your next assessments. Cumulative assessment demonstrated effectiveness when combined with interleaved reviews in Mariano's (2024) research, where the posttest served as preparation for the forthcoming End-of-Grade Assessment in Mathematics. The outcomes of the posttest offer a clearer understanding of students' requirements for upcoming reviews before the EOG. Consequently, the EOG Math outcomes closely resembled the posttest results. In the IR class, 11 of the 20 students passed the EOG, consisting of 3 students in Level 5, 4 students in Level 4, and 4 students in Level 3, with only 4 students categorized as Not Proficient. In the BR class, most participants (9 out of 15) were Not Proficient, with 3 students at Level 3 and Level 4, and none achieving Level 5.
Summary
Interleaved review is not a “one-size-fits-all” strategy and a prescription for a successful class reviews. This research proven strategy will work with teachers intentionality on students’ needs. The teacher must understand the students, their learning styles, strengths and weaknesses and interest in all stages of implementing this interleaved reviews. Success in state assessments is one of the duties of a teacher but it is our moral obligation to make learning mathematics interesting and relevant to their life experiences.
References:
Austrew, A. (2022, August 2). How to prevent your kids from losing what they learned in school during summer vacation. https://www.scholastic.com/parents/books-and-reading/raise-a-reader-blog/summer-slide.html
Briones, J. (2016, August 9). The importance of reviewing what you learned and how to review https://www.johnnybriones.com/blog/the-importance-of-reviewing-what-you-learned-and-how-to-review#:~:text=But%20say%20you%20don't,to%20make%20sure%20it%20sticks.
Covey, S. (1989). The 7 Habits of Highly Effective People. Google Books. https://books.google.com/books?id=upUxaNWSaRIC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58. https://doi.org/10.1177/1529100612453266
Keerthirathne, W. K. D. & Rajarata University of Sri Lanka. (2020). Peer Learning: an Overview. In International Journal of Scientific Engineering and Science (Vol. 4, Issue 11, pp. 1–6) [Journal-article]. http://ijses.com/wp-content/uploads/2020/11/151-IJSES-V4N10.pdf
Mariano, L. A. (2024). Effectiveness of interleaved practice in the achievement of Grade 8 students in mathematics in Chatham Middle School, North Carolina, USA. [MA thesis]. University of Northern Philippines.
Rohrer, D. (2012). Interleaving Helps Students Distinguish among Similar Concepts. Educational Psychology Review, 24(3), 355–367. https://doi.org/10.1007/s10648-012-9201-3
Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481–498. https://doi.org/10.1007/s11251-007-9015-8
Rohrer, D., Dedrick, R. F., & Agarwal, P. K. (2017). Interleaved mathematics practice: giving students a chance to learn what they need to know. http://uweb.cas.usf.edu/~drohrer/pdfs/Interleaved_Mathematics_Practice_Guide.pdf
Rohrer, D., Dedrick, R. F., & Burgess, K. (2014). The benefit of interleaved mathematics practice is not limited to superficially similar kinds of problems. Psychonomic Bulletin & Review, 21(5), 1323–1330. https://doi.org/10.3758/s13423-014-0588-3
DOI 10.5281/zenodo.17317123
