Tuesday, 25 February 2014

Helping students Master Facts

Coming from Junior grades I know that facts are important for students to help them with math.  In addition, I know that learning facts also helps students with solving problems.  However, whenever you talk to anyone this is such a bone of contention.  Some feel that facts are the most important parts of math and some feel they will be learned through problem solving and inquiry.  I tend to lie in the middle of these groups leaning moreso to the inquiry approach.  Don't get me wrong facts are very important to learn and are a critical part of mathematics.  They do help students; however, I also see the other part where students only know facts and cannot apply them to problems.  IN this case facts are harmful to students development because they keep trying to apply rote learning with no understanding.

So with this in mind what is a teacher to do?  I recently came upon some great advice from van De walle's book, Elementary and Middle School Mathematics: Teaching Developmentally.  In his book he has a whole chapter on mastering basic facts.  Van de Walle offers three components to learning facts and none are through strict drill and or quantity of drilling facts.

His components are:

1) Help children develop a strong understanding of the operations and of number relations.

2) Develop efficient strategies for fact retrieval

3) provide practise in the use and selection of those strategies

This is great but what does this look like in a classroom.  I can't say for others but in my classroom this is how I have interpreted these components.

Number sense is beyond just learning algorithms or memorized facts.  You need to understand how numbers work together, their significance, decomposing and composing, and other mathematical reasoning.  All of these help you with mental facts, which in turn helps you with mastering basic facts.  In my classroom, we do a variety of things:
                       a) String lessons: this is fifteen minutes before the problem where we practise mental facts.  These strategies relate to the problem and I hope that students start to apply them in the problem.  This might be adding by tens, using friendly numbers, adding with doubles, etc.

                      b) Problem Solving: chosing a proper problem is just as important to helping students learn math facts.  The problem you chose should allow students to practise their fact recall and not just a traditional algorithm.  In addition, when you debrief the problem there should be some talk about efficiency and using these facts.  This will promote student thinking in this area and see why its important to learn and use their facts.                       

                      c) Teacher Talk: Often when students talk about a strategy I will articulate with certain math talk.  So what you are telling me is this.... Your use of vocabulary will always assist student learning.  I also sometimes do think alouds of my thinking, to help student conversations.  This always is accompanied with talk about what students think I did.

                         b) Math games that focus on these skills.  All of our games in the classroom focus on certain skills.  It helps students practise their facts and learn about numbers beyond just pure memorization.  It also brings out talk among students and teacher.

In addition to this we also do math fact Mondays and Math game Friday.  During Monday my students do a "mad Minute" type of activity.  Though it is not truly a mad minute as it is more about practice of facts then of fast recall.  Students do have a time limit but it is more that it happens at the end of the day.  I will also like to say that my students asked for this activity and relish the moment when they can show me how much they have learned from the week before.  I give my students ten minutes to answer about 60 questions.  We also graph our results over the weeks and set goals for the next.  The emphasis is on goal setting and improving their individual learning.  Results are never shared among the students.  On Friday we do a whole period on math games.  This is important as it give students time to play and practise.  Even though that after finishing a problem they do get to play games not every child gets the same amount of time, this way they do.

Furthermore, Van deWalles chapter there are many great suggestions on the type of strategies that these things can bring out and is a read I recommend all teachers doing.

This only some of the things that I do in the classroom to assist in fact recall.  It is important but how you do facts is just as important.  How do you help with facts?  What type of activities do you use?  Love to here from you.


  1. Jonathan, I really liked this post of yours! I know that we've spoken about some of these ideas before, but seeing them in action today really helped me understand how everything fits together. I've recently started doing more work with math strings, and I love them! I liked how your students shared their thinking about the problems. I'm going to move to this model as well. Thanks for the idea!

    I also love the math games that you shared today. I tried to create some of my own that also have some connections to real world math. We'll see how things go. When it comes to math games, I think that getting at that "thinking" is so important. That's why I really liked the ones that you shared today.

    As for "Mad Minute," I'm still split on this. I don't think that I can go this route (even if it is students just competing against themselves). Looking at the needs of the students in my class makes me concerned. I'm worried about how the students would perceive themselves based on their own scores and the time that it takes (even without the comparison). I wonder if there's another way to practice these skills for those students that need it without the photocopied Mad Minute papers. I'm still thinking about this, and would welcome any suggestions!

    Thanks for giving me lots to think about! This is a post I'll be sharing with others too!

    1. I too was very hesitant about it. The funny part is I started it because of pressure from a school climate. I am not normally one to gave into the consensus, especially when I have research to back up my thinking; however I have been really surprised at the results and how much my students love doing it. Now, what are the factors for this. One is definitely the community but I think we also have done a lot around community and setting goals for yourself. It could also be that I love math so, do they.

      Will this work with every classroom, I don't think so but there needs to be a balance between practise and showing. Now are there other ways to show, yes. I think we could almost do a google docs template to this? What do you think? Also oral talk in games also gets this done.

      In the end the mad minutes is an experiment that so far has worked out. A. I still hesitant, yes. We will see how it goes.