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Posts Tagged ‘Teaching Fractions’

Ontario’s Mathematics program for Kindergarten to Grade 12 has just undergone a significant revision in the wake of the continuing decline in student performance in recent years. On June 24, 2020, Education Minister Stephen Lecce unveiled the new mathematics curriculum for elementary school students with a promised emphasis on the development of basic concepts and fundamental skills. In a seemingly contradictory move, the Minister also announced that the government was cancelling next year’s EQAO testing in Grades 3 and 6 to give students and teachers a chance to get used to the new curriculum.

While the Doug Ford Government was elected in June 2018 on a “Back to the Basics” education pledge, the new mathematics curriculum falls considerably short of that commitment. While the phrase “back to the basics” adorned the media release, the actual public message to parents and the public put more emphasis on providing children with practical skills. Financial literacy will be taught at every grade level and all students will learn coding or computer programming skills, starting in Grade 1 in Ontario schools. A more detailed analysis of the actual math curriculum changes reveals a few modest steps toward reaffirming fundamental computation skills, but all cast within a framework emphasizing the teaching of “social-emotional learning skills.” 

The prevailing “Discovery Math” philosophy enshrined in the 2005 Ontario curriculum may no longer be officially sanctioned, but it remains entrenched in current teaching practice. Simply issuing provincial curriculum mandates will not change that unless teachers themselves take ownership of the curriculum changes. Cutting the number of learning outcomes for Grades 1 to 8 down to 465 “expectations” of learning, some 150 fewer than back in 2005, will be welcomed, especially if it leads to greater mastery of fewer outcomes in the early grades.

The parents’ guide to the new math curriculum, released with the policy document, undercuts the “back to basics” commitment and tilts in a different direction. The most significant revamp is not the reintroduction of times tables, teaching fractions earlier on, or emphasizing the mastery of standard algorithms. It is the introduction of a completely new “strand” with the descriptor “social-emotional learning skills.” That new piece is supposedly designed to help students “develop confidence, cope with challenges, and think critically.” It also embodies the ‘discovery learning‘ approach of encouraging students to “use strategies” and “be resourceful” in “working through challenging problems.”

Ontario’s most influential mathematics curriculum consultants, bracing for the worst, were quick to seize upon the unexpected gift.  Assistant professor of math education at the Ontario Institute for Studies in Education (OISE), Mary Reid, widely known for supporting the 2005 curriculum philosophy, identified the “social-emotional learning” component as “critically important” because it would “help kids tremendously.” That reaction was to be expected because Reid’s research focuses on “math anxiety” and building student confidence through social-emotional learning skills development.

Long-time advocates for higher math standards such as Math teacher Barry Garelick and Ottawa parent Clive Packer saw the recommended approach echoing the prevailing ‘discovery math’ ideology.  Expecting to see a clear statement endorsing mastering the fundamentals and building confidence through enhanced competencies, they encountered documents guiding teachers, once again, toward “making math engaging, fun and interesting for kids.” The whole notion that today’s math teachers utilizing traditional methods stress “rote memorization” and teach kids to “follow procedure without understanding why” is completely bogus. Such caricatures essentially foreclose on serious discussion about what works in the math classroom.

How does the new Ontario math curriculum compare with the former 2005 curriculum?  Identifying a few key components allows us to spot the similarities and differences:

Structure and Content:

  • New curriculum: “clear connections show how math skills build from year to year,” consistent for English-language and french-language learners.
  • Former 2005 curriculum: Difficult to make connections from year-to-year, and inconsistencies in expectations for English-speaking and French-speaking learners.

Multiplication and division:

  • Grade 3, new curriculum: “recall and demonstrate multiplication facts of 2, 5, and 10, and related division facts.” In graduated steps, students learn multiplication facts, starting with 0 X 0 to 12 X 12 to “enhance problem solving and mental math.”
  • Grade 3, 2005 curriculum: “multiply to 7 x 7 and divide to 49 ÷ 7, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting) No explicit requirement to teach multiplication tables.

Fractions:

  • Grade 1, new curriculum: “introduced to the idea of fractions, through the context of sharing things equally.”
  • Grade 1, 2005 curriculum: Vague reference – “introducing the concept of equality using only concrete materials.”

Measurement of angles:

  • Grade 6, new curriculum: “use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise.”
  • Grade 6, 2005 curriculum: “measure and construct angles up to 180° using a protractor, and classify them as acute, right, obtuse, or straight angles.”

Graphing data:

  • Grade 8, new curriculum: “select from among a variety of graphs, including scatter plots, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs “
  • Grade 8, 2005 curriculum: “select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph”

Improvements in the 2020 Math curriculum are incremental at best likely insufficient to make a significant difference. Providing students with effective instruction in mathematics is, after all, what ultimately leads to confidence, motivation, engagement, and critical thinking. Starting with confidence-building exercises gets it all backwards. Elementary mathematics teachers will be guided, first, to developing social and emotional learning (SEL) skills:  (1) identify and manage emotions; (2) recognize sources of stress  and cope with challenges; (3) maintain positive motivation and perseverance; (4) build relationships and communicate effectively; (5) develop self-awareness and sense of identity; (6) think critically and creatively. Upon closer scrutiny these are generic skills which are not only problematic but also entirely unmeasurable.

The fundamental question raised by the new Ontario math curriculum reform is whether it is equal to the task of improving stagnating student test scores. Student results in English-language schools in Grade 3 and Grade 6 mathematics, on EQAO tests, slid consistently from 2012 to 2018. Back in 2012, 68 % of Grade 3 students met provincial standards; in 2018, the mean score dropped to 58 %.  In Grade 6 mathematics, it was worse, plummeting from 58 % to 48% meeting provincial standards. On international tests, Ontario’s Program of International Student Assessment (PISA) Math scores peaked in 2003 at 530 and dropped in 2013 to 509, then recovered slightly in 2018 to 514, consistent with the provincial slide (See Graph – Greg Ashman). Tinkering with math outcomes and clinging to ineffective “mathematical processes” will likely not be enough to change that trajectory.

Building self-esteem and investing resources in more social and emotional learning (SEL) is not enough to turn-around student math achievement. Yet reviewing the new mathematics curriculum, the Ontario curriculum designers seem to have lost their way. It all looks strangely disconnected from the supposed goal of the reform — to raise provincial math standards and improve student performance on provincial, national, and international assessments.

What’s the real purpose of the new Ontario mathematics curriculum reform?  Does the latest curriculum revision reflect the 2018 commitment to move forward with fundamentals or is it a thinly-disguised attempt to integrate social and emotional learning into the program?  Where is the evidence, in the proposed curriculum, that Ontario education authorities are laser focused on improving math standards? Will this latest reform make much of a difference for students looking for a bigger challenge or struggling in math? 

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