[Update – I’ve added a four more Quizlet study sets to my Multiplication Facts Practice folder. The three “Practice Doubling” study sets are designed to provide students practice doubling a number, a necessary skill to be able to efficiently use the Doubling Multiplication Fact Strategy The “Practice Halving” study set is designed to provide students practice halving a multiple of ten, a necessary skill to be able to efficiently use the Use-Ten Multiplication Fact Strategy.]
As a member of NCSM, I get a weekly email called the Marshall Memo that shares summaries of a variety of education-themed articles. What I like about the Marshall Memo is that I get exposed to articles I may never have encountered on my own. Even better, while many articles are on topics that aren’t math-specific, I’m still often able to able to make connections to my own work.
Take this recent article from The Reading Teacher, for example, called “More Than Just Word of the Day: Vocabulary Apps for English Learners.” I don’t have access to the full article, but in this summary, Marshall notes that the authors reviewed 53 free vocabulary-teaching apps for grades 3-8. Out of all these apps, Quizlet was the only app they endorsed. That piqued my interest!
It also connected to something I’ve been thinking a lot about lately, which is the strong research evidence that retrieval practice promotes learning:
“Retrieval practice” is a learning strategy where we focus on getting information out. Through the act of retrieval, or calling information to mind, our memory for that information is strengthened and forgetting is less likely to occur.”
https://www.retrievalpractice.org/
If you’re unfamiliar with the IES Practice Guides, they provide research-based recommendations on a variety of educational topics. In their guide Organizing Instruction and Study to Improve Student Learning, Recommendation 5b is Use quizzes to re-expose students to information. The level of research evidence for this recommendation is strong, according to the guide. It goes on to say,
“…quizzes or tests that require students to actively recall specific information (e.g., questions that use fill-in-the-blank or short-answer formats, as opposed to multiple-choice items) directly promote learning and help students remember information longer.”
IES Practice Guide, Organizing Instruction and Study to Improve Student Learning, page 21
This also brings to mind “Rachel,” a thought-provoking blog post from Michael Pershan that has had me thinking about the interrelationships between deriving and recalling facts.
Suppose a student has just derived 9 x 4. If they’re confident and successful, they might have an opportunity to share that solution with the class — I might ask them to share their solution, and they might have a moment where they ask themselves, “wait, what was 9 x 4 again?” This is recall practice. Or, maybe, they are working on a larger problem in which 9 x 4 is merely a step, and their later work calls on them to remember the product of 9 x 4. They derive it, and then turn back to the problem and ask themselves, “what was 9 x 4?” Or perhaps, while working on a large set of multiplication problems, a student derives 9 x 4 and is then asked to derive 90 x 4. They ask themselves: what is 9 x 4?
Rachel by Michael Pershan
All of this thinking got me inspired to give Quizlet a try for creating study sets that provide students practice both deriving and recalling multiplication facts. I organized my study sets around the thinking strategies shared in The Book of Facts: Multiplication, published by ORIGO Education.
“Research show that the most effective way for students to learn the basic facts is to arrange the facts into clusters. Each cluster is based on a thinking strategy that students use to help them learn all of the facts in that cluster.”
The Book of Facts: Multiplication, ORIGO Education
If you’re unfamiliar with these thinking strategies, ORIGO has kindly created a one-minute overview video of each one:
- Use-Ten Strategy for Multiplication
- Doubling Strategy for Multiplication
- Build-Up Strategy for Multiplication
- Build-Down Strategy for Multiplication
For each strategy I created three levels of study sets in Quizlet. Level 1 focuses on reinforcing the thinking strategy. As students practice the flashcards, they are presented a pictorial representation of the multiplication fact that reinforces the thinking strategy. For example, if students are solving 8 × 5, the reverse side of the flashcard shows the product as well as a visual that reinforces the idea that each fives fact is half of the related tens fact. In this case, the array model shows that 8 × 5 is half of 8 × 10.
Level 2 focuses on a verbal reminder of the related thinking strategy. The front of the card remains the same, but the back of the card includes a reminder of what students can think about to help them derive the fact. Here’s the back of the 8 × 5 card in Level 2:
Finally, in Level 3, the focus is on recalling the multiplication facts. The back of the card does not include any reminders; it just shows the product. If students get stuck, the teacher can ask the student to recall the thinking strategy they’ve learned, otherwise students should focus on recalling the facts.
In addition to the strategy-focuses study sets, I’ve also included three study sets that practice a variety of multiplication facts when students are ready to focus on recalling across all of the facts. Version 1 focuses on the x0, x1, x2, x3, x4, and x5 facts. Version 2 includes a wide variety of all facts. Version 3 focuses on the x6, x7, x8, and x9 facts.
You can access all 21 study sets on Quizlet. If you’re not familiar with Quizlet, there is a free version and a paid version. I’d recommend starting with a free account. If you’re a teacher, be sure to indicate it when creating your account because teachers get extra features.
Some words of advice, Quizlet offers a wide variety of modes for practicing study sets.
I’ve noticed that many of these activities show the product and students are supposed to answer with the multiplication expression. If you want to start by presenting the multiplication fact to the students, all you have to do is click the Options button and then change “Answer with” to “Definition” instead of “Term.” I recommend doing this because generally we want students to recall the product not the multiplication expression.
In the Flashcards activity, I recommend turning on Shuffle. If students are at a point of focusing on recall rather than deriving each fact, then I also recommend turning on Play. This will make the flashcard automatically turn over after a few seconds. This prevents students from falling back on counting strategies.
In the Learn activity, I recommend going into the options and deselecting “Multiple choice questions.” For retrieval practice, research does not recommend multiple choice questions. Rather, the “Flashcards” and “Written questions” are preferable Question Types for this activity.
In the Test activity, I recommend only the “Written” and “True/False” question types. Again, in all of these activities, don’t forget to change the “Answer With” option from Term to Definition.
And finally, if your students are not familiar with the thinking strategies in these study sets, then they may be very confusing and unhelpful to students. In The Book of Facts series, ORIGO recommends four teaching stages:
- Introduce the strategy – Hands-on materials, stories, discussion, and familiar visual aids to introduce the strategy or sub-strategy
- Reinforce the strategy – This stage make links between concrete and symbolic representations of the facts being examined. Students also reflect on how the strategy or sub-strategy works and the numbers to which it applies.
- Practice the strategy – This stage aims to develop accuracy and increase ‘speed’ of recall. In this stage, a range of different types of written and oral activities is used.
- Extend the strategy (to greater numbers) – Students are encouraged to apply the strategy to numbers beyond the range of the basic number facts. The activities in this stage are designed to further strengthen students’ number sense, or “feel” for numbers.
The Quizlet study sets I created fall within the Practice stage. If you’d like to teach these strategies to your students, I do recommend checking out The Book of Facts: Multiplication because it provides several activities at each of the four stages for each strategy.
If you try out these study sets with your students, let me know how it goes! I’m excited to be able to share this resource for retrieval practice to the teachers in my district. If I hear feedback from them, I’ll be sure to let you all know how it goes.
Teaching to the Beat of a Different Drummer 