In addition to working on rich problems to address various mathematical process expectations, we’ve also been trying to close the gaps in mathematical understanding, and develop automaticity, based on our observations in class and the data from previous years' EQAO results. One way we are doing this is by calling all hands on deck (including in-school Spec Ed and ESL teachers, and even our principal), and working once a week with smaller groups of students (2-10 kids per group) on areas of need in the number sense strand, as determined by student results on diagnostic assessments from a resource called “Leaps and Bounds”.
While more proficient students work on deeper problems to stretch their thinking and improve their communication skills, other students work in smaller groups on tasks that address their specific weaknesses.
My own little group of three has been working on comparing and ordering numbers this month. We’ve been dealing with numbers up to 100, using hundreds charts, number lines and base ten blocks to scaffold the learning, and make things more concrete.
I am frightened by how big the gaps are!
Today, one of the tasks involved
While more proficient students work on deeper problems to stretch their thinking and improve their communication skills, other students work in smaller groups on tasks that address their specific weaknesses.
My own little group of three has been working on comparing and ordering numbers this month. We’ve been dealing with numbers up to 100, using hundreds charts, number lines and base ten blocks to scaffold the learning, and make things more concrete.
I am frightened by how big the gaps are!
Today, one of the tasks involved
finding numbers that were greater than one number, and smaller than another number. For example, the students had to make and/or write a number between 54 and 78. One student wrote 82, another 49. When I suggested they have another look and see, both of them randomly guessed other, also incorrect numbers! It seems that not only do they not understand the concept, they are also unable or unwilling to reason through the “problem” to see if what they have written makes sense.
It is taking all my strength not to roll my eyes or let the frustration show in my voice as I gently encourage my little group to think through the question to make sure they understand it, to check and see if their work make sense, and to prove that their responses are reasonable and accurate.
Truly, I am stunned by how many apparently basic pieces seem to be missing from some students’ understanding! Last week, one of them told me that 38 was greater than 72, because the former had more ones!!!
Although we continue to do our best to meet the needs of the extremely wide variety of learners in our classrooms, I am scared for some of our students with weaker understanding, and I am more than a little frustrated that they don’t seem to have had some of the basic home experiences that my own children have had, of calculating how many forks to lay on the dinner table when a friend comes to visit, for example, or counting apples in the cart at the grocery store, or checking to see who has more raspberries in his bowl at breakfast.
Sometimes my optimism diminishes, and I feel truly hopeless: How can our hard work possibly impact years of mathematical neglect?!
It is taking all my strength not to roll my eyes or let the frustration show in my voice as I gently encourage my little group to think through the question to make sure they understand it, to check and see if their work make sense, and to prove that their responses are reasonable and accurate.
Truly, I am stunned by how many apparently basic pieces seem to be missing from some students’ understanding! Last week, one of them told me that 38 was greater than 72, because the former had more ones!!!
Although we continue to do our best to meet the needs of the extremely wide variety of learners in our classrooms, I am scared for some of our students with weaker understanding, and I am more than a little frustrated that they don’t seem to have had some of the basic home experiences that my own children have had, of calculating how many forks to lay on the dinner table when a friend comes to visit, for example, or counting apples in the cart at the grocery store, or checking to see who has more raspberries in his bowl at breakfast.
Sometimes my optimism diminishes, and I feel truly hopeless: How can our hard work possibly impact years of mathematical neglect?!