picture courtesy Washington Elementary School, PA
Accuracy, speed, process, meaning…these are all words that have been passed around the age-old discussion of math time tests. Do students need to be able to prove their worth with sixty multiplication (or addition, subtraction, division) facts completed in five minutes? Three minutes? What is fast enough and what is the purpose of this practice? This is a question I ask often, why are we doing this? Finding the answer is the trick.
Conceptual math programs are being used throughout schools today with a focus on understanding the method and being able to explain the process of mathematics. I have been using a conceptual math program for over 10 years, half of those with first grade and half of those with fourth grade. I see my students truly understanding math processes and reasoning behind what they are doing. I see them explaining their thinking. I also see them struggling as they make simple computational errors. They have been taught the strategies of number computation and given hands on activities to practice, but it seems many of them have not had enough time or expose with practicing to become efficient.
There is a need to be able to compute 8×6 quickly and accurately when working on a problem. In the past, I have given three-minute tests and asked students to memorize the facts to be able to compute quickly. This method is not great, but students need to be able to compute numbers accurately. I need to know who needs further practice. I know this is not best practice, but it fits into the allotted time and schedule of my classroom. It is a request from administration to show what students know. It fits into the grade book and parents understand the scores and can help students practice at home. Imperfect, but what is the answer.
This year our district has done a lot of reading and discussion on time testing and we found a system that answers that question, why are we doing this? Students are timed to discover which strategies they need more exposure to. This information is used in a meaningful way for students at school and gives parents better information at home. In class we are working through the facts in sequence of strategies. Identity property is first followed by the fives. Then we work on doubles and fours (double the double). Next are the threes and sixes and nines. That leaves the sevens and eights for the end. Zero and ten can work in at the very beginning or after the twos and fours. The students are expected to get 100% before they move on. They fill in their multiplication chart (addition, subtraction, or division) to show mastery and see what their focus is as well as the facts they know.
So how is this so different? Students are given focused flashcards to keep at their desk; these can also be sent home, to practice after having a mini lesson on the strategy. These strategies have been taught and used whole class, but some students need a small group refresher with blocks, arrays, and more time to practice. Having students work through the strategies gives them a better understanding and a focused practice on the skill instead of the old school memorization technique. I have seen this transfer into our conceptual math as students catch their mistakes and feel comfortable grabbing a multiplication table for the facts they know they don’t know. Teaching them metacognition, thinking about thinking, is a secondary lesson that has arisen from this new process.