A Balanced Math Program

With the endless humdrum of the math wars happening, it is easy to forget that what teachers really need is simple help to understand practical ways to improve or acknowledge their math program.  We have heard both sides for decades. One side is about the context and deeper conceptual understanding while the other side worries about the basics. To be fair there really shouldn’t be any sides. Mathematics is a combination of both concepts and procedures. Even more realistic you will never find a teacher that doesn’t do both.

I love this picture from one of the presentations that Matthew Oldridge and I do on this topic:

Screen Shot 2017-10-16 at 12.07.09 PM.pngWhat it shows is a continuum of teaching. At times, we may be closer to the fully guided while at times we do some unstructured unguided lessons. However, most of the time we are some where near the middle. For myself I lean more towards the 3/4 mark of the line.

A couple of years ago I wrote a post about a balanced math class but since then I’ve had some small tweaks that I thought would be useful to highlight.

When I first thought of this subject I thought of six things that should be in the program (you can read about each section in my post):

  1. Guided Mathematics
  2. Shared Mathematics: Students work together to “Mathematize”
  3. Conferencing/ Monitoring
  4. Congress
  5. Reflection
  6. Math Games and Math Facts

Now my opinion about these things haven’t changed I still think you need to have all of these components but I want to simplify a bit and think more about the practical side.  For this reason I want to steal a little line from the Leaf’s Head Coach Mike Babcock, think of a five day block of time.

Now, before I go into detail I want to preface that this is just my opinion and in no way is this the only way. I think as teachers we need to have professional judgement to choose what is best. I also don’t expect to have these ideas prescribed like a five day must follow. I just want you to reflect on these components.

I broke it into five days because I really felt that it was easy to look a five day segment in time. Some times these components may take more time or less but on average I try hard to stick to this.

Day 1: Problem Solving

I am a firm believer that our math program should be predominately a place where students are problem solving and exploring math concepts. During this time, the teachers role is to explore the concepts with the students. It is a fine balance between a guided approach for some to a more let kids explore. As a teacher I am also conferencing, questioning and monitoring students work. I am checking it to landscapes of learning and thinking about how I will debrief the learning. What misconceptions are students having? How are they tackling the problem? What collective conclusions are they making? are all questions that go through my head.

Day 2: Congress

This to me is one of the most important things we can do in a math class and where that shared, guided and explicit instruction is happening. During this time, I am questioning and explicitly linking the math concepts to their problem solving. Where I may allow students to wander a bit in exploration I am tightly keeping the reigns around the big ideas and misconceptions I observed in the problem.

Day 3: Number Talks

These have been one of the best decisions that I have made as a teacher. Number talks allow me to discuss strategies, talk through misconceptions and help students visually see the mathematics that is happening around them. Number talks is also a 15 to 20 minute exercise so they happen frequently and often in the classroom. Another great aspect is that it allows students to communicate and talk about math in a meaningful way.

Day 4: Reflection

The more I read about this topic the more I believe that this needs to be integrated more in the classroom. We need to explicitly show students how to reflect about their learning and how to set goals in order to improve. This year in my class I have purposefully set time aside for students to regularly talk about their math learning.

Day 5: Purposeful Practise (Math games, Centers and regular practise)

Yes I said it Purposeful practise. This may be in a worksheet but if it is I hope it is geared toward each child’s needs. For me purposeful practise is about seeing where a child is developmentally and finding things that may work for them. This year it has been center work, using board games or math games and digital games like knowledgehook and Mpower.  The important part is understanding that it is purposeful and meaningful.

Overall, I think we need to think less of this war between concept and procedure and meet in the middle. How can we help our students learn and build bridges mathematically.

I would also love to hear your thoughts. If you have any opinions or questions please feel free to leave a comment.

Here is my slide deck on a balanced math approach.

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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.