math facts Archives - Shelley Gray

Three Easy Ways to Transform Scary Mad Minute Drills into Something Purposeful

Shelley Gray — Sat, 06 Aug 2022 15:23:01 +0000

Yes. Learners need to know their math facts. Why? As they get older and mathematics becomes more rich and complex, working memory needs to be freed up for problem-solving. Retrieval of these facts needs to be automatic. This is just like a reader recognizing sight words as a part of literacy development. Unfortunately, curricula expectations and Common Core standards all over Canada and the United States prescribe that learners be able to “recall” or “know from memory” certain math facts by certain grades and the emphasis on timing (read: speed) and pacing becomes too heavy.

Remember Mad Minutes? When I was in Grade 4 we had one minute to recall 50 multiplication facts. My teacher actually coached me on how to improve my speed by alternating the direction I answered the questions in so I wouldn’t waste time resetting my arm from right to left! While I did commit my facts to memory that year, it wasn’t until I started teaching and tutoring that I realized how problematic drills like these are and how they reinforce the narrative that fast = best instead of the importance of fact fluency.

In his 2015 TEDTalk on mastery, Sal Khan uses a great analogy to highlight the importance of self-paced mastery in learning. He describes how silly it would be to build the first and second floors of a home if the foundation is still wet and not to code and then argues that it is equally detrimental when we as educators “artificially constrain” the time learners have to master something – especially when we feel pressure to (or are mandated to) move on before they are ready.

Given the tumultuous landscape that education has been (come on, all life has been) since the COVID-19 pandemic, and with many people going on about learning loss, I wish we could let go of our grip on timing. I know, I know… easier said than done and the district/administrator/state tests are coming for you by the end of the next school year. But this brings me to my main point about drilling math facts if you are going to drill at all: timing should not be the end goal. When it comes to memorization, it’s not about when, but how (Fosnot & Dolk, 2001).

Disclaimer: you shouldn’t be thinking about drills or rote practice with math facts unless you have already been teaching for understanding.

That being said, if you are looking for some simple repetitive practice, here are three simple shifts you can make to modify those scary mad minute drills into something more purposeful:

DRILL SELECTIVELY; NOT EVERYTHING ALL AT ONCE

By grouping and sequencing instruction and practice around small clusters of related facts, rules, or properties, we create more opportunities for learners to make connections between operations and see patterns and relationships between numbers. An example of this would be a drill solely including questions related to multiples of 2, 5, and 10.

BASE ACCURACY ON THE ATTEMPTED QUESTIONS AND USE A STOPWATCH, NOT A TIMER

If the learner attempts 30 out of 50 questions, score their drill out of 30 not 50. Also, have the clock run up and not down. If they answered 17/30 correctly in 6 minutes and 28 seconds, co-create a SMART goal for the next drill that focuses on accuracy first. When they can correctly answer all of the questions, then set a goal to reduce the time. Celebrate progress, personal bests and let the learner record their score.

USE ERROR FEEDBACK TO INCREASE FLUENCY

Look at the questions that the learner answered incorrectly or didn’t attempt. Look for instructional opportunities. With the clock turned off, review appropriate strategies they could use next time and bring it back to sturdy conceptual understanding using concrete manipulatives and visualization of special relationships.

So, to drill or not to drill? How do you boost fluency and work towards automaticity in your classroom?

References

Cholmsky, P. (2011). From acquisition to automaticity: The Reflex solution for math fact mastery. Retrieved July 28, 2022 from https://www.reflexmath.com/images/Reflex_White_Paper.pdf

Fosnot, C. T. & Dolk, M. (2001). Young Mathematicians at Work: Constructing Number Sense, Addition and Subtraction. Portsmouth, NH: Heinemann.

How to Teach the Doubles Facts So Your Students Actually Understand

July 15, 2022 No Comments

What are the doubles facts in math? How do you teach them? Why are the doubles addition facts important? By the time you finish reading

Fun Multiplication Games for 3rd and 4th Grade (help them master the facts)

July 12, 2022 No Comments

How can you make learning multiplication fun while also allowing your students to master the multiplication facts? WITH GAMES! Multiplication games are an effective way

How to Teach Math Effectively Using the Concrete Representational Abstract Model

July 16, 2020 7 Comments

WHAT IS THE CONCRETE REPRESENTATIONAL ABSTRACT MODEL? The CRA Model is an instructional approach for teaching math. It consists of three phases: Concrete Representational Abstract

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Growth Mindset and Math Facts: Success for Every Student

Shelley Gray — Sat, 23 Sep 2017 23:53:27 +0000

We hear a lot these days about growth mindset. We see it all around us on anchor charts, posters, and in the hallways. But growth mindset in the classroom has to be about more than simply telling our students that they can do hard things. We have to infuse the growth mindset into everything that we teach if we really want our students to develop and use it.

First of all, let’s discuss a few benefits of growth mindset. We know that students with a growth mindset rather than a fixed mindset are more resilient and more excited to learn new things and take on challenges. We also know that students with a growth mindset truly believe that they can get better at something through learning. Students with a growth mindset see mistakes as an opportunity to learn, rather than as a failure.

Simply having a growth rather than a fixed mindset can have a huge impact on student success.

However, we face challenges with the growth mindset when it comes to math:

Parents often project their own attitudes about math onto their children. This happens all too often where children are told, “I was no good at math when I was in school either,” by a parent. This is projecting a fixed mindset onto the child, where he believes that because his mom/dad was not successful with math, he will not be either.
Lack of success. Think about the students that you teach who hate math. Do they experience success on a regular basis? Do they see themselves as able to do the work? Growth mindset is all about challenging students to do difficult work and being motivated to do so. But we have to make sure that our students can be successful too. Success leads to motivation.

We can get past these challenges! Here are a few tips for infusing growth mindset into your teaching, particularly when it comes to math facts.

Ensure that your students understand that their brain can grow stronger. Tell them, “Your brain is like a muscle. The more you use it, the stronger that it gets!” As your students succeed in areas where they used to struggle, point it out! Say things like, “All of your hard work really paid off,” “Can you tell that your brain is getting stronger in this area?”, or “Remember how hard the 9’s facts used to feel? Now they are easy for you! Your hard work and great attitude is really working.”
Praise the effort, not the ability. Praising the ability, for example, “You are really good at math!” will encourage a fixed mindset. Praising the effort, for example, “You worked so hard to understand this, and you did it!” will encourage a growth mindset. Students will be more motivated to take on new challenges when they are praised for their effort.
Keep your standards high, but still ensure success on a regular basis. Your students need to feel successful and able. You can do this by providing work that is achievable, but still challenging. When you teach multiplication, don’t begin with the hardest facts. Start with the easiest ones. Let your students know what it feels like to be successful. It’s a great feeling! Then you can increase your expectations once you see that they are ready for the challenge.
EMPOWER your students. This can be done through providing lots of choice, and allowing students to be in control of their learning. Everyone loves the feeling of being in control of themselves, your students included!

Are you using Math Stations to teach math facts in your classroom?

If you are using any of my self-paced, student-centered Math Stations for basic facts, this is a great way to infuse growth mindset into your classroom! Growth mindset is built right into the stations (which is why students find them so motivating), but here are a few quick tips that will help you even more:

When you do the oral test with a student, take a second to talk about the set of facts that she just finished. Did it feel challenging? Did it feel easier as she kept working at it? Did she do anything special to make that particular strategy or set of facts easier to learn?
When a student is beginning to learn a difficult strategy, talk to him about how exciting it is to take on a new challenge! Remind him how past levels felt hard at first, but then got easier as he worked at it.
Use effort-based praise. Rather than, “You are really good at the partial products strategy,” you might say, “I can sure tell that you have been working hard to understand the partial products strategy! You’re getting fast! That hard work is paying off. We are going to have to find you some more challenging activities to do pretty soon!”
Have students use their personal tracker progress charts to see just how far they’ve come and think about where they are headed.

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Free Mini Course: Basic Multiplication and Division – Mastery for ALL Students

Shelley Gray — Sun, 02 Jul 2017 15:36:05 +0000

Sorry, this mini course is no longer available. However, I have a wealth of information on my website about teaching the basic multiplication facts. Start HERE with effective strategies for basic multiplication.

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