Computational Fluency, Learning, Math, number sense

Student Inquiry into Computation with Cuisenaire Rods

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At our last math community meeting teachers were given an opportunity to explore the provocation shown above.  This provocation was provided to support wonder, curiosity, creativity and multiple opportunities for computation.  Teachers were able to create designs with addition, and multiplication using one of my favorite computation manipulatives…Cuisenaire rods.

I chose this activity and these manipulatives for many reasons.

  • It allows students to explore part-part-whole thinking
  • It provides opportunities for multiple computations in an engaging way
  • It brings creativity, and design into mathematics
  • It allows for collaboration, and conversation
  • Students can discover relationship, and multiple interpretations

After our professional exploration many teachers took this activity back to their classrooms and shared it with their young mathematicians.  Below are some examples of what the students came up with in classrooms.

As a follow up students can bridge the concrete to abstract continuum by recording their computations/designs pictorially and abstractly on a sheet.  Initially, recording sheets could have pictures of coloured rods to match the concrete representations the students created.  As students progress in their level of abstraction they can switch to just marking the value on the rod.  Abstractly, they would record the equation their design represents.

Below are some supports that can help you incorporate Cuisenaire rods into your classroom.

Student Desk Cards

Whole Numbers

Decimal Numbers

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Build It! Draw It! Write It! Student Recording Sheet

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Math, Teaching and Instruction

The Mad Minute- A Tragic Tale of Defeat and Remorse

Once upon a time, in a land not so far away there lived a girl named Jennifer. Jennifer was a student and on this particular day she was sitting in her desk carefully writing her name on the back of a piece of white paper. When her teacher said GO and not a second before (it was strictly forbidden to peek) she turned over her paper to reveal a page full of math basic facts. As quickly as possible, she began computing math facts and writing the answers on the paper. The whole class was silent, the only exception was the quite sounds of pencils frantically scratching and the odd moan. The gauntlet had been thrown down and the race was on to conquer the sheet and then celebrate your triumph in front of your friends. After two minutes the class was told to stop..turn the page over and put their pencils down. Some students smiled with victory as the teacher walked between the rows collecting the sheets. Some students hung their heads defeated, deflated and quite frankly exhausted from the effort. Jennifer lived in both groups some days she felt the sweet sensation of victory, some days the sheer agony of defeat. On this day the sheet, only half completed had declared it’s victory over her. The teacher would return the worksheet the next day with X’s and checks marks on it, along with the final score out of 50. Students who did well were told to keep up the good work. Those who didn’t were told to try harder next week when Mad Minute day came. On this particular day Jennifer asked her teacher if they had to have Mad Minutes day every week. She was given this short, simple answer…”It will help you learn your basic facts”.

Years later Jennifer was a teacher, with her own group of students sitting before her eagerly awaiting their signal to turn over the sheet of paper and begin. She had been given the most wonderful opportunity to teach students their basic math facts and was using the one tool she knew would ensure that students learned… The Mad Minute. After all, she had successfully learned her basic facts and had long since abandoned using her fingers and toes…well most of the time anyways. Some of her students experienced success, some struggled, some downright refused to start. Jennifer reflected on this fact with a colleague the next day. Why didn’t the kids get it?…she was doing all she could…she had even increased her Mad Minute time to twice a week…yet they refused to learn. Her colleague suggested sending the worksheets home for more practice. Maybe parents would have the time to help the students continue to learn those basic facts. After all they had now completed the unit on operations.

As I reflect on this story I feel sad, for that young girl who felt defeated, that young teacher who knew very little about teaching mathematics, and for all of those students. I was that girl and knew how defeated the Mad Minute made me feel…yet I created that same experience for my students. I simply knew no other way. A few years later I heard a speaker say something that really struck home to me… “When teachers align what they teach… with what students learn…and with what they assess… they honour the learners in their classrooms.

Mad Minutes, at least the way they had been modelled for me, were considered the one stop shop for teaching students to learn and assessing progress in basic facts. Knowing what I know now I understand that they are none of those things. They didn’t teach…they evaluated, they didn’t support learning…they evaluated, at best you could say they assessed and provided feedback for teacher planning and instructional decision-making (which they didn’t). At worst…they evaluated. They became an activity for survival of the fittest. The strong survived to basked in their success. The weak were defeated, crushed and left to feel like math failures. No one was honored. If you were one of those bright-eyed, trusting students in my classroom…I sincerely apologize. You deserved a teacher who would teach so that you could learn. A teacher who would assess and use those assessments for learning. A teacher who would not send home the very object of your frustration only to have you experience failure in a new environment. You deserved better! Knowing what I know now…I COULD do better. I now believe that:

  • Teaching mathematics is about developing student competence AND confidence
  • Teaching of basic facts should be done in a way that is strategic, and in attainable steps that can inspire confidence
  • Practice should be purposeful and targeted
  • Fluency is important and students should be given opportunities to develop fluency that is built on a foundation of conceptual knowledge
  • Monitoring of Progress is key and should inform instructional decisions
  • Assessments can be timed if necessary but students should be allowed to finish and only “compete” with themselves
  • Students should be given opportunities to see patterns within operations and connections between addition/subtraction and multiplication/division
  • Numbers are flexible and teaching/ learning about them should be as well

My next few posts will continue to develop my thinking on purposeful practice and procedural fluency in a way that I hope honors our learners and inspires success. As always your comments and feedback are always welcome.