I was right in the middle of grading papers during my planning when I overheard the fifth grade math teacher across the hall. Keep in mind this is a regular occurrence. I love her dearly, but she does have a tendency to get excited and…a bit…loud while teaching. She asked a student (one of mine from last year) something about area models. He responded with, “Mrs. Swinford didn’t teach us about area models last year.”

My jaw dropped to the floor. We spent weeks on area models with multiplication and division. Naturally, I had to march across the hallway and remind him that yes, I did teach about area models. Keep in mind this was all playful and we had a good relationship. After a little prompting, he did remember something about area models after all.

This isn’t isolated to just math. When I was teaching third grade, a fourth grade teacher let me know that one of my former students told her that she had never heard of a verb before. Ugh.

All of this is to say that our students forget content. Fortunately, we’ve come a long way in learning how students remember. In fact, we know that there are three stages of learning.

Three Stages of Learning:

• Encoding – when we get information in and absorb knowledge.
• Storage – where we hope that once we encode information, our knowledge sticks around.
• Retrieval – when we reach back and bring something we previously learned to mind.

Not too surprisingly, the bulk of classroom instruction centers around encoding-when we present information to our students. During this phase of instruction teachers may focus on lecture, videos, games, tasks, or read alouds. Students may reread, highlight information, play games, or review notes to study and review content. While none of these things are bad, they are part of the encoding state and lead to short-term learning.

One of the best ways to make sure students remember is to focus on the retrieval stage, rather than the encoding stage of learning. It’s important to recognize that just because students know something once doesn’t mean they will always remember it.

As you read, keep in mind that YES, learning must extend past memorization of facts. But, students’ basic understanding of information improves students’ higher-order thinking and learning, and transfer of knowledge.

Retrieval Practice is Key in Helping Students Remember What They Learn

Retrieval practice is when students bring something to mind or pull information out of their minds. This practice occurs when students recall and apply multiple examples of previously learned content or skills after a period of forgetting.

When implementing retrieval practice in the classroom, it is essential to keep the practice as a no-stakes opportunity for students. It is not an assessment. Instead, it is a learning strategy.

Brain Drain

One easy strategy to allow students to practice retrieval is a Brain Drain. As you are teaching, pause and ask students to write down everything they can remember. Then resume the activity or lesson. There is no need to collect papers, grade, or even discuss.  If you love research, you can read more about this strategy. It’s technically called free-recall and is very common in brain research. This strategy boosts students learning, organization of knowledge, and reasoning.

Two Things

This is a way we can use retrieval practice to break up our lessons quickly and easily. During a lesson have students write down two things any any specific prompt: What are two things you learned so far today? What are two examples from your own life that this relates to? What are two things you’d like to learn more about? Once again, remember this is a learning strategy, not an assessment.

The Countdown

This is a way to incorporate a variety of retrieval practices. Students reflect on five things they remember from the lesson. They ask four questions about the content and share three things they would like to learn more about, which requires them to retrieve what was taught. They also think of two situations or real-life examples the content made them think of, and they write the one thing that surprised them most.

Retrieval Guides

These are extremely similar to study guides or guided notes. The difference is that students fill these out AFTER the lesson is taught, rather than DURING the lesson. Of course, after students complete the guide conduct a discussion to make sure students have the correct answers. This strategy also helps teach students how to pull out important information from reading a text.

Another thing to keep in mind during retrieval practice is that practice before a lesson helps students for short-term memory. Retrieval practice after a lesson is beneficial for long-term memory.

Spacing

Most all teachers know the importance of review spread over the course of the year. Teachers also recognize that students cannot review content for one or two days and be expected to remember and recall that content. This need for review is due to “spacing”.

Spacing is a combination of retrieval practice multiples, over time. The key to spacing is completely counterintuitive to most teachers. For the most efficient practice, students must have time to forget content. What!?!

Spacing things out and coming back to them increases learning by using forgetting. When we let time pass, students’ knowledge has time to settle. This space gives students the added benefit of savings, which is when students return to something they have learned before and experience the “aha” moment. With that savings, students’ can retrieve knowledge more fluently and quickly.

Interleaving

Interleaving is the strategy of mixing things up during spacing. It’s simply re-arranging the order of retrieval opportunities. Without interleaving, students are able to plug and chug without thinking about strategies. this is often called “blocked practice”. With interleaving practice, students must choose and retrieve the appropriate strategy for each problem. It’s also important to mix similar things or ideas that require students to carefully apply a concept. Keep in mind, having students present one concept in different ways is not an example of interleaving. Also, mixing different subjects does not increase student learning, because the content areas are too different.

Spacing and interleaving work hand-in-hand, and it’s often difficult to separate the two. Fortunately, it’s really not necessary to discern the difference. This is one of the reasons I love using my review resources. New content is added after it is taught and past content is continuously reviewed.

Feedback & Metacognition

Metacognition is often difficult for students to develop. In fact, students often think they know something, when actually, they don’t. Also, students are often overconfident when they predict their own learning.

Feedback is the absolute best tool for increasing and improving students’ metacognition.

• Students must receive feedback on correct and incorrect answers. Without that feedback, students may retrieve information they think is correct and develop a false sense of confidence. Feedback is important on correct answers, because some students may have guessed correctly and also need that affirmation. That’s one of the main reasons I added “Or Surprises” to the assessment reflection form.

• Both immediate and delayed feedback benefit students. One of my favorite ways to incorporate both is by going over answers on a review together. That provides immediate feedback. Then, the following day, I pull small groups based on the review’s data and we go in further detail on the problems students missed.

More than likely these are all things you already do in your classroom. I have found that I need to be intentional in adding these strategies to my plans, because it’s easy to skip over some of these steps. To help you out, I’ve included a free download of several of the pages shown above. Download your copy here.

What are other strategies you use in your classroom to encourage retrieval and spacing?

The post Teaching So Students Remember appeared first on Ashleigh's Education Journey.

Strategies for multiplication are so important for students. As a math teacher, multiplication facts have always been a source of concern. We know that a deep understanding of multiplication is essential for students, but there is also need for students to have at least a moderate (ideally more) memorization of multiplication facts, as well as strategies for multiplication.

The past several years, I’ve used my own resources along with online programs such as Xtra Math to help students learn their multiplication facts. However, I developed a couple concerns with these programs.

One concern is the stress that I see it cause students. Many children, especially the ones who struggle with memorization and/or anxiety, appear to become frustrated by the timed aspect of the quizzes.

The other concern is that I don’t see a lot of math fact progress with my struggling students, even with ample practice time in class. While all students can certainly learn and improve, some students need alternative strategies for multiplication and approaches, rather than solely focusing on memorization.

This digital multiplication program provides an alternative solution. It can be used along with any of your favorite existing resources or math curriculum.

This multiplication strategies program is broken into 5 parts. Each day of the week students complete a different task based on the math facts they are currently practicing.

Monday-Build It

On Monday, students create a grouping model for each set of facts (2×2, 2×3, 2×4, etc.), and grouping models are an important strategy for multiplication. They allow students to visualize and “see” multiplication.

To create the grouping model, students drag the larger circle to indicate the number of groups. In the example, there are two groups, so the student drug two large circles to the slide. Then, students drag the squares to show the quantity in each group.

Students will repeat this process for each set of facts.

Tuesday-Matching Representations

On Tuesday, there are three matching pages for students to complete. This allows students to begin thinking about visual representations of multiplication, which is also important strategies for multiplication.

For each set of facts students drag a written description, array, repeated addition problem, and a multiplication equation to a single row. Each page has three rows and all the needed cards are included on that page, so students will not have to copy and paste any cards.

Strategies For Multiplication – Wednesday-Multiple Representations

On Wednesday, students use the slides to create multiple representations of each set of facts, rather than match representations.

Students drag a square to a hundreds grid to show how to skip count. Then, they type a repeated addition representation. Students then drag blue squares to build an array of the fact. The last step is to drag an arrow to show multiplication on a number line.

Multiplication Strategies – Thursday-Word Problems

It’s incredibly important to incorporate word problems throughout your instruction and to not wait until the end of the unit. This allows students to understand multiplication in context, which supports strategies for multiplication.

In this activity, students solve to multiplication word problems (that use that set of facts) and then they write two word problems using that set of facts.

Multiplication Strategies – Friday-Game

On Friday, students move to a more abstract multiplication with a multiplication game. The game will focus on the multiplication fact of the week. If students don’t have a partner, they can play color vs. color.

Daily Check-Up

The last item of each day with the digital multiplication program asks students complete a daily check-up. It’s a timed test with a twist.

Students click on the link to go to a Google Form where there is a short quiz. They must get each question correct before moving to the next question.

Before beginning the quiz, students are prompted to start the included timer. Students are prompted to stop the time when they finish the quiz.

Then, students slide the colored tab on the graph to indicate how long it took them to complete the quiz. Students will only take one quiz a day and by the end of the week, they can see their progress.

Implementation Ideas for the Digital Multiplication Program

If you’re teaching third grade, you may want to assign program this to all students. I would not begin this practice until after the concept of multiplication has been introduced to students. However, it’s necessary to wait until the very end of the unit to begin implementing strategies for multiplication.

If you’re teaching fourth or fifth grade, you may want to give a pretest for each set of facts. You could easily use one of the Google Forms for the pretest. Then, only assign each set of facts to the students who need the extra practice.

You could pace students with one set of facts per week and pretest as you begin each week. You could also have all students work at their own pace with some students practicing 2 facts, some 3 facts, and others 4 facts.

Whether or not you grade each page is completely up to you and your expectations. I plan to use this as an instructional tool, not an assessment.

This can be incorporated into morning work, math centers, a skills block, remediation program, or even homework. There is definitely no one right way to implement this program.

It is recommended to teach multiplication facts in the following order. However, once again, it’s entirely up to you.

• 5 facts
• 10 facts
• 2 facts
• 4 facts
• 8 facts
• 3 facts
• 6 facts
• 9 facts
• 7 facts

Rather than create a new resource, I added this digital multiplication program to the existing print Multiplication Program. That way you will have access to both. If you already own it, you can download it again (at no cost) for the update! Students will greatly benefit from these strategies for multiplication.

If you don’t already own it and would like to test it out, click the link to download the 2 facts for FREE here!

The post Strategies For Multiplication appeared first on Ashleigh's Education Journey.

Teachers agree that memorizing multiplication facts is such a challenging part of elementary school. In fact, I surveyed more than 20,000 teachers about their biggest challenge in math instruction. The most overwhelming response was that their students don’t know their math facts. This issue is a not a new trend. Math facts, especially memorizing multiplication facts, has been a hot topic since I was in elementary school. I still remember taking “mad minute” tests as a child where we had to solve a certain number of problems in one minute.

We now know that teaching multiplication strategies through games and hands-on activities is more beneficial that repetitive drill. When using games to encourage memorizing multiplication facts, it’s essential that the games and activities are intentional and follow a specific framework. To help me stay focused, I’ve created a series of systematic lessons and activities students can use to memorize and understand multiplication facts. You can find those lessons in my TpT shop.

In this post:

• Multiple Representations
• Tiered Flashcards
• Multiplication Strategies Booklet
• Word Problems
• Timed Test

Multiple Representations

The first step in memorizing multiplication facts is for students is to SEE the different representations of the math facts. For example in this multiplication activity, students sort arrays, repeated addition number sentences, and equations. This allows students to begin understanding what the multiplication means.

Memorizing Multiplication Facts – Tiered Flashcards

After students sort multiplication representations, they should then progress to leveled flashcards. This is another helpful step in memorizing multiplication facts. At this point, students aren’t ready for traditional abstract flashcard practice. Instead, students should begin with the set of Build-It flashcards. In this set, students actually build each multiplication problem. They could use counters or snap cubes for this activity. After students have concrete experience, they can move to pictorial models of each multiplication problem as a flashcard. This pictorial model helps bridge concrete and abstract thinking. In the third set of flashcards, students can answer the multiplication problem using an abstract strategy.

Multiplication Strategies Booklet

When memorizing multiplication facts, students should also have the opportunity to WRITE about the strategies they use to solve multiplication problems. This allows students to internalize their learning. For each set of facts, students describe a strategy they could use to solve a multiplication problem. If I have a student who has already worked their way to automaticity in that set of problems, I ask students to explain to a friend how to use a strategy. Students also represent problems using arrays, repeated addition, grouping models, and a number line.

Memorizing Multiplication Facts – Word Problems

It’s so important to teach memorizing multiplication facts in context, so for each set of facts that students work though, be sure to have them solve AND write multiplication word problems. This is another reason it’s so important to have students write about the strategies they use. For example, if students are working on their four facts they will solve two problems where four is a factor and write two problems where four is a factor.

Timed Test

While timed tests can be misused, they can also play a positive role in memorizing multiplication facts. Rather than giving students a certain amount of problems to solve in a set amount of time, I have students solve the entire set of multiplication problems and time how long it took to complete all of the problems. This alleviates the extra stress that comes with a timed test. I also have students graph how long it took to complete the test to encourage metacognition and self-reflection. I staple multiple versions of the set of facts to the timed test graphing sheet to give students four different opportunities to take the test.

To help keep my students organized with each of these activities, I give them color coded bookmarks. The bookmarks show what is expected from students each week. The activities are listed in the order in which they should be completed. As students complete an activity, they check it off on the day it was completed. You can see these activities in my TpT shop!

I did add a few extras at the bottom of each bookmark, because these are things we do weekly, if not daily. I send home a Weekly Multiplication Game with students every Monday. These memorizing multiplication fact games only require dice or a set of playing cards, which I provide if students don’t have at home. This isn’t an assignment to be graded. Instead, it’s an opportunity for fun practice.

I also give students who need additional support a Multiplication Fact Booklet that will take them through each multiplication problem for that set of multiplication facts. This gives students the extra support they may need and it solidifies understanding.

Xtra Math is another great practice tool. However, it’s important to keep in mind that it is a tool. Nothing replaces the conceptual activities where students actually work with multiplication facts.

You can read additional posts on memorizing multiplication facts here and here. I’d love to hear about what you’ve tried that has been successful!

The post Memorizing Multiplication Facts appeared first on Ashleigh's Education Journey.