Lessons Learned from Our Research in Ontario Classrooms. 1. Intro. The cultural activity of teaching - the ways in which the teacher and students interact about the subject - can be more powerful than the curriculum materials that teachers use. (Lewis, Perry & Hurd, 2004).
Justification for Using the Number Line evidence suggests that classroom practice has changed little in the past 100 years. (Lewis, Perry & Hurd, 2004)
Using pre-partitioned shapes in teaching and assessing can mask an incomplete or incorrect appreciation of fractions as relational numbers.
Many teachers are unaware that students are adopting only part of a regional “part of a whole” model of fractions. That is, some students focus on the “number of pieces” named by a fraction and others the “number of equal pieces” named, without addressing the relationship between the area of the parts compared to the area of the whole region.
Gould, Outhred, Mitchelmore
No matter what the situation, children defaulted to pizzas or pies…
We had to teach another method for comparing fractions to move them forward…
Fractions on Stacked misconceptions…
Tad Watanabe, 2002 TCM article understanding to check student
What we are learning: understanding to check student
• We know for sure that students are using circle representations even when it doesn’t make sense mathematically or contextually.
• That fractions is an enormously difficult area to teach partly because it is incredibly difficult to learn (misconceptions of students)
• Certain representations seem to be underutilized even though they appear to be helpful to students. Linear models for representing fractions have an important place in Ontario classrooms – when and how does it help kids (discrete, linear, area models)