They Just Don’t Know Their Facts

They Just Don’t Know Their Facts…

I’m pretty sure I’d be rich if I had a dollar for every time a teacher has said that to me. To be fair, I’m pretty sure I’d be rich if I had a dollar every time I said it in my career. But, when you know better, you do better, so here is what I now know.

My career started as a student teacher in 1998. That was the first time I heard the complaint about not knowing facts. The answer was always – they need to practice their flash cards at home. If only they practiced. If only their parents made them practice. If only they weren’t lazy. If only they cared about school. If only they paid attention.

“If only” and “just” may be the enemy words of progress and innovation. It takes complete responsibility off of the person saying them. I started to realize this later on in my career, and began listening carefully to those words. These are the words of oversimplification, of self justification, and of saving face in front of a situation that seems out of hand.

“Yet” is the new buzzword. So, “They just don’t know their facts” turns into “They just don’t know their facts yet.” It’s an improvement for sure – a growth mindset that might lead to some new learning around how students “know facts.” It still boils math down to “just” – a word that continues to scare me. Are these students really just one flashcard away from knowing their facts? Or is there something else that we haven’t considered?

My new recent learning is sadly not “new” at all. I hope that the more people that share learning, the more rapidly it spreads, so that we can stop blaming the students and start finding the solutions.

Fact Fluency Through Games, Not Timed Tests

First, if you haven’t read Jo Boaler’s Fluency Without Fear, then stop right here and go read it. If she doesn’t convince you to stop giving timed tests, then I’m not sure what will. However, for those beginning the journey away from timed tests, the easiest entry point is to practice with games. Her “How Close to 100?” game is actually a lot of fun, even as an adult playing with students. Plus, when you get kids playing games, they now have an independent activity that frees you as a teacher to confer with students, hear their math explanations, and probe thinking.

Games engage students to build fluency while simultaneously building number sense.

In my career, games became my initial step away from timed tests. If they weren’t going to memorize them from timed tests (anxiety, lack of feedback, practicing wrong answers…) then wouldn’t they memorize them from play?

Sure. For many students, the games did the job of practice and developing fluency. For others, they needed a different kind of help. I relied on multiplication charts to help them out when we were learning a different concept that needed the fact fluency to be there so that their cognitive energy was freed up for the other thinking. Why teach what a computer can do inevitably faster than a human can?

Yeah, but…

“Not everyone has a grid in front of them to draw a picture, and they need to be able to do problems like 342 x 74 with relative speed.”

“They are still failing their math tests.”

“They won’t have a multiplication chart on the SBAC.”

“I don’t have time for these games when I need to get through the textbook.”

Hmm. 🤔

So these are questions I had asked myself at one point, and then asked others, and now have others ask me.

The Math Wars in the 1980’s and 1990’s created some serious debate over the role of technology in math. I think the Common Core does a good job bridging this debate – students must be able to understand number relationships. If we focus on that development of number sense, then we truly can rely on technology for the speed piece. If we neglect the sense making, then no technology is going to support our work.

So let’s focus on the statement, “They are still failing their math tests.” I have been spending time giving the IKAN and GLOSS assessments from the Georgia Numeracy Project, which has based their work on NZMaths from New Zealand. For background info and directions for assessment, check out Graham Fletcher’s page here. The IKAN written assessment gives numeracy stage scores in 4 domains – Number Sequence & Ordering, Fractions, Place Value, and Basic Facts. Which one do you think was the lowest? Which was the highest?

Out of every class I’ve scored (at this point I’ve scored 12 classes of about 28 kids each), every single class had the highest score in Basic Facts, and the lowest score in Place Value. Now I realize that this is in no way scientific research, but the trend is fascinating. Maybe we are missing the point when it comes to “they don’t know their facts”?


What is going on behind these facts and this place value idea? Here is the document I’m currently digesting:

Now I’m putting my fourth grade teacher hat on, and I’m thinking, but this seems so basic? The thing is, do we really know that our students have had enough experiences with number to move them through this trajectory? If my students don’t know “know their facts”, then can they visually recognize something like this:

Can they tell me what one more is (without recounting)? One less? Yes? What about this? How far away is it from 10? From 0? Can they tell me two numbers that make up this number? Do they see the 3 and 2 or the 4 and 1? Yes? Then what about this?

And why do things like this need to be searched for and even bought from TPT, when they should be free to all? Under my fourth grade teacher hat, which up until a few years ago didn’t have this knowledge, all of this seems like too much. Just have a go with the flashcards and don’t be lazy. But I know better, and now I do better. The thing is, in the classroom, I affect 28 students for one year. How do we spread this knowledge, so that all teachers are armed with the understanding, as well as armed with the materials and skill to dig deep into children’s mathematical understanding?

The Basics of Fact Fluency

Procedural fluency is skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

Common Core State Standards Initiative, 2010

Flexibility • Efficiency • Appropriate strategy use • Accuracy

There’s the definition . Does a timed test measure any of these? How do you know? Before you can say, “They just don’t know their facts,” we have to carefully reflect on this definition. How did we prepare them for flexibility in choosing strategies? How did we prepare them for accurate calculation? What did we do to help them understand efficiency? And how have we spent our time to help them see appropriate strategy use vs. ineffective strategy use?

In conclusion, dig deeper.

We have decided upon some screeners (including the GLOSS along with the IKAN, as well as some ideas from Build Math Minds) to get at some answers to these questions. Yes, many of these are one on one, but when in doubt, ask the students! The interview process can take some time, but it is enlightening to find out how students are thinking – not to mention on the job professional development for the teacher. If we can understand where a breakdown in understanding has happened, we can intervene more precisely. I’m also interested in doing more work with math Running Records, which involves more interviewing to understand what strategies students are using to add, subtract, multiply, or divide. If our end goal is for them to be fluent but flexible with numbers, then it would help us to know where their current level of understanding is.

In the meantime, my fervent hope is that teachers take the time to do Number Talks (or Fraction Talks) every day. I’m not sure there is a more powerful way to help students explore number relationships. For our teachers, we are working on a repository of resources so that Number Talks are not something they have to spend lots of time searching for – the resources will be at their fingertips. Games will also be provided so that teachers can easily pick from games that will not only engage but help students build number sense.

For me, I’m working on coming up with a more straightforward answer to “They just don’t know their facts.” This post is a start, but nowhere near a final version! I’ll be seeking out more understanding with my colleagues, with Twitter, with the research, and most important with the students we serve. Would appreciate your comments below!

Math Writing at Empower 19

ASCD Empower 19
Chicago, CA
March 16-18, 2019

Just got back from Chicago, and have so many thoughts rolling around in my head!! Blog ideas about navigating the conference, Ron Clark, Doris Kearns Goodwin (this is my new role model – her storytelling, her presence, her speaking ability and intelligence are all qualities I aspire to), presenting do’s and don’ts, and writing ideas are all swirling around in my head. So, in trying to stay focused, I’m starting with my big passion – communicating mathematically.

There were few workshop options in the math writing/communicating world, and the first one I went to was titled Elevating ELL Discourse in the Mathematics Classroom, presented by Sherry Ayala and Sylvia Olmos. Although the title didn’t reference writing, the summary did. Much of this workshop turned out to be similar to work we have done in our district around the 5 Practices. Lately as I’ve attended workshops, I’ve noticed quite a bit of similar learning, which leads me to look for the “nuggets”, or the new piece of learning that I can attach to prior knowledge. In this case, my nugget was how we teach and practice math vocabulary.

Students partner up, and explain their thinking around a problem, such as 324 – 165. As a teacher, you’ve considered what vocabulary they may use around this problem, such as subtract, add, ones, tens, hundreds, regroup. You provide the students with a small table, so that the listening partner can tally the number of times the partner used the vocabulary words.


From there, the listening partner can paraphrase back to the speaker what s/he said, and the speaker can self assess. Why didn’t I use regroup (or ones/tens/hundreds/etc). Did I need to? How could I explain differently so that I could use a different vocabulary word? I’m super curious to try this out in a classroom to see how students respond. The vocab words chosen are all based on what you have taught and what you expect them to use – being aware that the flexible thinkers you have molded will likely be able to find ways to explain that would change the vocab you are looking for.

The other workshop I went to was titled Strategies for Teaching Effective Mathematical Communication, from the book by the same name, presented by Laney Sammons and Donna Boucher. This one intrigued me because it was directly on mathematical writing, and I’m searching for different research based opinions and ideas to round out the work we have been doing so far. Again I saw many similar ideas to what we have already been doing with discourse (oral communication ideas, using CRA in math progressions). I noticed that this workshop also brought up the idea of developing math vocabulary, including the use of the Frayer model (along with a foldable that I’ve referenced in many of my own trainings).

Another nugget from this workshop was the inspiration to redo our criteria on our rubric. Their suggestion, based on work from the Ontario Ministry of Education, was to examine:

  • Precision regarding details, strategies, observations, and calculations
  • Explanations of assumptions and generalizations made
  • Clarity in logical organization
  • Cohesive arguments presented
  • Elaborations that explain and justify mathematical ideas and strategies
  • Appropriate use of mathematical terminology

I think that this list makes for a nice set of criteria beyond what we have used up to this point, and the work now will be to blend it with our current rubric:

So what is next for my math writing partner in crime and myself? We are looking at streamlining our presentation so that the focus is not the lessons that are prepared for classes, but instead an approach more linked to disciplinary literacy. An approach in which the vocabulary is introduced, clearly understood and practiced. One where there are multiple criteria for success and we can narrow lessons down to one or two of those criteria each time to develop, strengthen, and support their communication in writing. Plus, we need to go over the book, Strategies for Teaching Effective Mathematical Communication, to look for more ways to refine our thoughts and our rubrics.

The last nugget, that I should probably save for my navigating the conference post, is: Just because you didn’t attend the session doesn’t mean you can’t spy on the notes! So the Connecting Math and Literacy session by Alex Kajitani was at the same time as another session. In his presentation, he had this wonderful quote from Marilyn Burns. Besides wondering why I hadn’t seen it before, I was struck by the clarity it brought me.

Writing in math class isn’t meant to produce a product suitable for publication, but rather to provide a way for students to reflect on their own learning and to explore, extend, and cement their ideas about the mathematics they study.

Marilyn Burns
Educational Leadership, 2004

Spoiler alert – that one will be in our next presentation. Thanks to all who developed and presented at the conference! You challenged us to develop and refine our own thinking, and I am grateful for it.