At The Toronto Heschel School, we take a critical thinking approach to numeracy.
As human beings, we are thinkers, not calculators. As noted in the Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario, “Making sense is at the heart of mathematical literacy. Mathematically literate students understand what they are doing and why they are doing it.”
The traditional approach to teaching math focuses on rote memorization, computational skills, standardized procedures, and coming up with the correct answer. At Heschel, we don’t aim to ingrain computational procedures designed to simply procure an answer, but rather instill a disciplined process to train mathematical habits of mind. This inquiry—or discovery-based—approach aims to increase fluency in number sense, improve problem-solving skills, and focus on deep understanding.
Some of the mathematical habits of mind that we work towards at Heschel include:
Our mathematical goals are ultimately for students to be able to conceptualize, approximate, be specific, be precise, and reflect. To conceptualize, students will think through simple scenarios, tell visual stories, or devise kinesthetic exercises (such as: “what does it feel like to walk 100 m?”). Math games, where the rules are strictly related to the concept being taught, allow students to apply or induce various concepts through practice. Students enjoy playing the games while developing their speed and accuracy in applying the concept, thus deeply absorbing the learning.
Elegant strategies for approaching math problems, which can be done quickly mentally instead of laboriously on the page, are introduced systematically. An example would be “Perfect Pairs,” whereby equations are considered in terms of what numbers will get them to a rounded multiple of ten and what is remaining to get to the answer. Strategies are introduced through inductive reasoning, whereby students observe data and apply their existing knowledge, and then they are given a name for the strategy. Students practice the concept and skill simultaneously through “strategy-builders”: games, activities, worksheets, and regularly doing mental math. In this way, students develop the mathematical habits of mind that develop their numeric literacy.
Learning mathematics is more than manipulating symbols and numbers. It involves fluency with how numbers combine, break apart, group and regroup, as well as investigation into the relative size of numbers and the relationships among them.Malka Regan and Ricki Wortzman
by Greg Beiles
Teaching for Understanding in Math Class
by Malka Regan and Rick Wortzman