Analysing student responses

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Through discussions with students during administration of the diagnostic assessment, teams gained additional insights into student understanding of fractions. In later sessions, teachers discussed the trends in their students' responses based on observations, moderated marking, analysis of student work and classroom video. As expected, younger students had fragile understandings of the meaning of a fraction, the relationship between the numerator and the denominator, and equivalent fractions. It was surprising that these understandings continued to be a challenge for some students through grade 7. Many students in grades 5 and 6 demonstrated a limited understanding of the connections between improper fractions and mixed numbers and had difficulty comparing them. Many students also had difficulty extending their fractions understanding beyond commonly used benchmark fractions. There was also a reliance on circles for representing and comparing fractions.

Another observation was that there was very little difference in diagnostic results for students in the same grade across the different classrooms and school boards, regardless of the perceived strength or weakness of the class.

Based on the collective strengths and area of need for each group, the focus for each exploratory lesson was identified. The foci included questions such as:

• What do students understand about fractions? How do they represent fractions? How does student understanding of representations allow them to better communicate their knowledge of fractions?
• How can we ensure that our students are engaged in thinking and reasoning with a variety of fractions, including proper, improper and mixed numbers?
• How can we deepen students' understanding of fractions using representations and connections between representations, thinking about what fractions are and what they are not, and thinking of a fraction as a number?
• How do we best develop understanding of the multiple meanings of fractions?
• How can we get students to use representations as tools for their thinking?