11 Dec Oh the Facts They Don’t Know!

Oh the Facts They Don’t Know

No matter where I go, what state I am in, or the demographics of the district or the school, I am asked the same question, “But what about when they don’t know their facts?”

I agree, knowing math facts sure does help other skills or concepts in mathematics feel easier.

I agree, having fact automaticity is preferred and a goal.

Can students still access grade-level mathematics without their math facts?

Yes. A billion times over, yes.

Math fact mastery should not be the gatekeeper to other mathematics.  Students who don’ t know math facts aren’t incapable of doing grade-level content.

You’re a 2nd-grade teacher and your students are struggling with multi-digit addition and subtraction.  It sure would be nice if they have their basic facts.

You’re a 5th-grade teacher and you are working on dividing multi-digit dividends by double-digit divisors.  Or you are teaching adding and subtracting fractions and need students to find common denominators.  Both are amongst a list seemingly a mile high of skills that require math fact mastery.

We can do this and we can do it without shaming our students nor becoming teachers likened to Cruella DeVille.

There is something crazy that starts to stir in us when we realize ‘once again’ students don’t know their facts.

Here are 10 ways to help students who don’t know their facts but still have to do grade-level work:

1. Know what facts they DO know.

Essentially, there are 36 multiplication facts.  When you take out commutative facts (3X6 is 6 X3) you are left with 36.    Instead of broadly declaring at every chance you get, “They don’t know their facts!”  Let’s ground the statement in the fact.  Like the actual math facts they don’t know.  I think you might be surprised at what you find.

Once we identify what they DO KNOW, we can focus on the facts that they don’t.

2. Give them a multiplication or other number chart (if addition/subtraction) and block off the products of the facts they DO know with a sharpie. Number charts like this one,  have some real benefits by showing the full equation for each fact and color-coding the product to see patterns.  The issue with most charts is that students begin to overuse them and use them even when they know the fact.  Marking them off will remind them. ”Hey! I know that fact, I don’t need my chart!”
3. Modify the problems. If we are focused on the learning processes such as long division, then I don’t want all of the working memory to be used on coming up with a math fact.  So, choose problems when you are first introducing a process (long division, double-digit multiplication, multi-digit subtraction with ungrouping, finding common denominators, etc.) that are on the friendly fact list  Friendly facts are the facts students know with ease so that they can be successful with the actual grade level skill.   Being more selective about your problem choice will help everyone. Bouncing around between various factors uses a lot of working memory for students who are struggling with fact retrieval.   Why not make their problems today with divisors of 2, 5, 9, (or whatever facts they know).
4. Be strategic. If you are modifying problems to include the factors students know, then add in a factor that students DON’T Know, like 6s. Once students understand the PROCESS then start to include problems with other factors so that students learn what to do when the DON’T know that fact.  But be strategic.  Don’t throw all of them at them.  If we want them to actually get better at their facts, we need to be strategic. Add in problems with 4’s for the students who are still working on their fours.  This will require them to work with fours many times during one lesson— improving the likelihood that he/she will gain more automaticity.  Mixing in all the facts is just too taxing and not as helpful.
5. Practice count bys. Like a lot.  See my post on using counting during transitions.   If we are being strategic, then count by’s is an important skill.  If you’ve selected problems with 4’s, for example, then practice count by’s. Before starting the group of problems, students list their multiples on their paper for easy retrieval during the solving.  This allows the student to focus on the problem steps and not on fact retrieval.  Going back and forth between steps in a procedure and coming up with a fact is often too much for students who are struggling.  We need to give them a way to be successful.
6. List the foundation facts. If you are working on adding or subtracting, and students are specifically struggling with their teen addition, have them list their ten + facts, doubles or other facts that will help them with the focus facts down their paper or their make ten facts for easy retrieval.  Same reasoning as above in #5.   For example, maybe they are working on multi-digit addition, but you’ve identified they don’t know doubles plus one facts.  Then have them list their doubles down the side of their paper to retrieve during the solving process.  Not knowing their doubles is partly why doubles plus 1 isn’t working. Of course, giving them a chart would help as well, but when they can’t use their chart, they need to practice creating their lists.
7. Put in intentional and strategic practice. During a CORE lesson isn’t the greatest place to do this work. You need to focus on grade-level standards during CORE instruction, but you need to have another place where fact mastery IS the focus. A  station, reteaching center, homework, intervention groups, etc. focus on the facts they don’t know.  Can we all agree that saying ‘practice your facts’ is a bit CRAZY?  For students who don’t know their facts, practicing all 36 ( and by the way, what does that even look like), isn’t being as intentional as we could be.  Of course, playing games helps students work on all facts, but what if we were even more intentional?  What if we helped them to really work on one set of facts at a time.  Let’s take 6’s as an example.  A student is struggling with 6’s.  If they are playing games for homework, let’s say a dice game, have one of the die always be a 6.  They still play the game, but they are also only practicing their 6’s.  OR, take a blank die or cube, like these, and write in the digits you want them to practice.  Maybe it’s factors they know and one new one they don’t know.  Maybe you program a die to have 6, 5, and 2 on the sides.  The other die might be a regular one.  So when they roll the die, one factor will always be either 1) one they know or 2) practicing the fact (in this case 6) that they don’t know.  Consider addition.  Students are working on counting on before they are working on other derived facts such as doubles plus one.  One of the die then is programmed with a 1, 2, 3, or 4 so that each other number that is rolled we are actually practicing counting on over and over again with 1, 2, 3,  or 4.
8. Focus on strategy. During lessons where we are no longer focused as much on the process—we’ve learned the process and now we’re practicing, we need to make room for teaching students how to navigate problems that include facts they don’t know. Of the steps above, we’ve covered almost all of the phases students go through but we need to add in strategy work.  Students need to practice derived strategies to become more fluent with a fact.
   1. Implement number talks using these facts. Number talks would happen at the start of a lesson, not necessarily during, but would help students build these skills. Have students work on flexibly thinking through how they would get that answer.  This will simultaneously improve fact mastery.  The more they use strategies, the more fluent they will become.
   2. Teach explicit strategies and model them in class. Not sure about fact strategies?  For multiplication, don’t you worry, I have you covered.  You can get your printable of many commonly used strategies here.  Let’s take our 6s example.  If the problem was 6 X8, have students”
      1. Recall- what’s the answer?
      2. If we didn’t know the answer, what could we try?
         1. Counting bys/ Multiples (let’s do it, let’s write them on our paper, etc).
         2. 5’ short cut. I don’t know 6 X 8 but I know 5 X8 = 40, so if I add another 8 I get 48.
         3. Use a fact I know. I don’t know 6 X 8, but I know 3X8 = 24, double it and I get 48.
9. Normalize tools. Model using the tools and strategies above.  Students have to feel safe to use them and to not be embarrassed by them.  When I’m working through a problem with students, and I say how many 6’s are in 48?  I wait for students to tell me 8, but then I quickly model a few other strategies (“Or, if we didn’t know we could do our count by’s, try them with me: 6, 12, 18..)  “If we didn’t know, we could use our chart.  Let’s try it” (teacher models how to use the chart). This takes mere seconds but gives access to EVERYONE.
10. Focus on productive strategies: In essence, this means stop unproductive practices that are further harming our students.
    1. We would never intentionally shame students.  I think it happens unintentionally and out of our frustration.  We are just trying to do our jobs and it becomes complicated when students are lacking skills they need to access our grade-level content.  But, posting our math facts publicly, as explained in this post,  saying things like, “C’mon guys, you should know these facts by now….” Etc. are shaming students.  When we do this, we put additional pressure on their hippocampus, which controls working memory, and now that student isn’t retrieving that fact even if they know it.
    2. Timed Tests. Thomas Edison:  Doing the same thing over and over but expecting different results is the definition of insanity.  Giving timed tests are not actually helping students who don’t know their facts.  If they did, students would know them.  The ones who don’ t know them aren’t actually getting any better with timed tests.  The only thing being practiced is memorization and if we are honest, it’s not working.  Try the strategies above instead.  Or read more here from Jo Boaler out of Standford on this issue.
    3. Avoiding grade-level content to teach facts.  We think kids aren’t ready for grade-level content due to lack of fact mastery, when in fact they CAN do grade-level work when given the right scaffolds.  The point is that a scaffold is intended to be released, so while giving students a scaffold, we simultaneously need to be working on releasing the scaffold through teaching the fact strategies explicitly and mostly outside of our CORE instructional block.

If we don’t spend time discussing strategies, we aren’t helping the fact mastery problem.  Memorization is not the only way.

Have we fully addressed this issue?  No.  Is this a good start?  You betcha!  But what am I missing?  What would you add to this list or what information do you need next?  Let’s continue the conversation in the comments or meet me on one of the social media platforms.  I’m on them all and would love to continue this conversation.

Don’t forget to get the freebie math fact strategy sheet! 

P.S. Do you teach Math Expressions?  Be sure to join my private facebook group? Check out the facebook live video from this week (December 9th) for a walkthrough of many of these ideas.

P.S.S. Not a teacher of Math Expressions? No problem, follow my facebook page, Empower Consulting to receive similar videos.