Interleaving or Spiraling Math

Interleaving or Spiraling Math

Repetition may be the key to mastery but some methods are more effective than others. Block practice in a math class is repetition of one skill and it works for short term recall but not long term retention. Another form of repetition to help with retention of prior knowledge is to use a spiraling or interleaving style of homework and/or assessments. Spiraling and interleaving are similar but they serve slightly different purposes. Both methods help students consider how they are thinking and how they practice remembering. They also help teachers identify where the gaps in understanding are individually and as a class. Both help save time on revision for assessments. Jane has used Spiraling in Middle School and Josie plans to use Interleaving this next year in High School but both techniques can be used at either grade level. Here are our ideas:

Spiraling (as used in Middle School) is an opportunity for students to revisit concepts so they stay proficient over an extended period of time. Spiraling means frequently assessing a series of pre-determined skills.  You begin by thinking of your course as a set of skills corresponding to state standards. (We had 30 skills for 7th grade but it could have been fewer.) Skills are the tools students need to solve more challenging problems. Dan Meyer came up with this assessing style. 

Assess:

Skill 1

Skills 1 & 2

Skills 1,2, & 3

Skills  2,3, & 4 (1 has dropped off after being assessed 3 times) 

This does take some time, and you may do it on a smaller scale simply starting where you are and writing a quick quiz or exit ticket consisting of problems from your last three lessons. I started this in the spring one year and just wrote a quick quiz at the end of the day for the next class and continued this way. I put the quiz on the board and the students wrote their work on a piece of paper. I printed copies for those who needed it. 

We now have  a structured set of common formative assessments in place for this year. They are very quick to grade and provide timely feedback. Students keep track of how they have done on each skill in a chart. They then know what they know & what they need to work on. They can ask for help on a specific topic like ‘solving 2 step equations’ versus just saying “I don’t understand”

Interleaving (as will be used in High School) is an opportunity for students to revisit concepts as they are learning new ones. When interleaving problems, you want to make sure that the skills you interleave are related, but not necessarily presented in the order in which they were learned. You mix the old with the new. You can use interleaving with other learning strategies. It requires students to first choose a strategy before they can solve each problem. This is often the hardest step. Interleaving strengthens students’ ability to interpret problems and then proceed to solve them.

When assigning homework, it is ideal to avoid block practice as that is most effective for short term memory. Textbooks tend to be written in block practice form, so you can interleave homework by choosing questions from a variety of lessons. This may take time for students to adapt to and for the teacher to pull together. It may be simpler to interleave homework by creating  your own worksheets or to search for mixed-review mathematics worksheets online. 

Other uses for spiraling or interleaving at any grade level:

• Stations: Set up stations with different types of questions. This way students need to decide what strategy to use for each problem. This is a good review for a unit assessment.

• Assign students to write questions for the assessments, solve them and tell how they would assign points. You can assign topics or let them choose. If they are good, use them on the assessment.

• Having students create (as a team) a Quizlet, Kahoot or Quizziz game is a good way for them to recall what they have learned. Again, it would help to give them a list of topics you want them to review.

Please share any strategies you have found to be successful.

Resources:

Rohrer, D., Dedrick, R. F., & Stershic, S. (2014). Interleaved Practice Improves Mathematics Learning. PsycEXTRA Dataset. doi:10.1037/e528942014-240

Meyer, D. (n.d.). How math must assess [Web log post]. Retrieved from http://blog.mrmeyer.com/2006/how-math-must-assess/

Meyer, D. (n.d.). The comprehensive math assessment resource [Web log post]. Retrieved from http://blog.mrmeyer.com/2007/the-comprehensive-math-assessment-resource/

Rohrer, D., Dedrick, R. F., & Stershic, S. (2014). Interleaved Practice Improves Mathematics Learning. PsycEXTRA Dataset. doi:10.1037/e528942014-240

Frequent Quizzing

Another Quiz?

Yes, another quiz!

Frequent “low-stakes quizzes” have been found to increase students’ ability to retrieve prior learning from their memories.  In addition to increasing students’ ability to retain and retrieve their math knowledge, some of the benefits include:

• giving students quick feedback allowing them to know how they are progressing in class
• building confidence - students are given multiple opportunities to succeed
• lowering stress - lower point levels have a smaller impact on student grades

While this strategy offers some clear advantages for our students, it can be challenging to implement.  Common concerns include the time to write multiple assessments, increased time grading, and how to find the time to give retests.  Here are how we have been able to work this strategy into our classrooms.

Middle School / Jane

We, a group of five seventh-grade math teachers along with a math interventionist, have created a list of skills needed by the end of 7th grade math. The students take a formative assessment (FA) after we have covered each of these skills - once or twice a week. They are given 3 chances for each skill. The FAs spiral: skills 1 and then 1,2 and then 1,2,3 and then 2,3,4 and then 3,4,5 etc. This lessens the pressure. If a student has shown mastery of a skill, they don’t need to take it again. This motivates some students to be careful on their FA. Students like this process so much that they will remind me if I have forgotten to give a FA. They feel that the FAs are an integral part of class versus something punitive. This also helps when we get to the summative assessment. 

High School / Josie

I was able to try out this approach in an algebra one class unit on systems of equations.  Much to my dismay, I found that many students were already having difficulty remembering how to graph linear equations.  So I began writing and giving tri-weekly “quick quizzes” to the class.  Each quiz had only two to three problems and was designed to take no more than 10 minutes of class time (often less) and be quick to grade. 

I am thrilled to report that the overall student achievement as well as student engagement were very high in this unit.  While many students’ groaned about the extra assessments, many agreed that taking the quizzes helped them to understand and do better on this unit.  Based on this experience I plan to make up quizzes for some additional units next year. 

How Can This Help You

If you don’t have the time or resources to develop multiple quizzes, start small. Pick one unit that your past students have struggled with and write two quizzes per week of that unit.  You don’t have to commit to the whole year to try out this strategy.  We have both seen positive results and hope that you will too!

See our references for further reading and the research behind this strategy and the resources page as possible sources for quiz questions.

Sources

Brown, P. C., Roediger III, H. L., & McDaniel, M. A. (2014). Make It Stick: The Science of

      Successful Learning. Cambridge, Massachusetts: The Belknap Press of Harvard University

      Press.

Frequent, Low-Stakes Grading: Assessment for Communication, Confidence. (2016, December 08). 

Retrieved from https://www.facultyfocus.com/articles/educational-assessment/frequent-low- stakes-grading-assessment-for-communication-confidence/

Low-stakes testing. (n.d.). Retrieved from https://www.oswego.edu/celt/low-stakes-testing

Low-Stakes Assignments. (n.d.). Retrieved from https://resources.depaul.edu/teaching-commons/teaching-guides/feedback-grading/Pages/low-stakes-assignments.aspx