Understanding graphs – does metacognitive questioning help students develop and refine their mathematical ideas?

This digest found in

What sorts of conceptual problems did the students have?

As background to the study the author described research into students' understanding of graphs, constructivist and cooperative learning, metacognitive instruction and students' "alternative conceptions" (beliefs and understandings that diverge from generally accepted models) of graphs. Some of the conceptual difficulties that students showed when interpreting or constructing graphs related to:

confusing the height and the slope;
putting in only one point;
treating a graph as a series of point by point changes rather than as representations of a continuously changing situation; and
regarding all graphs as representing positive relationships.

The researcher suggests that these alternative conceptions (or misconceptions) limit students' ability to develop what she refers to as 'graph sense'. She quotes research that suggests that 'graph sense' means students looking at the entire graph, or the relevant part of it, and understanding that it expresses the overall way in which two variables change in relation to each other.

Your path: Home > Welcome to The Research Informed Practice Site (TRIPS) > Themes > Thinking skills > Understanding graphs - does metacognitive > What sorts of conceptual problems did the students have?
Research Home Themes \| Find digests \| About the digests resources glossary researchers contact TRIPS Introduction What sorts of conceptual problems did the students have? How did the intervention affect students' mathematical understanding? What was classroom discourse like and how did it differ between the two samples? What classroom activities did the intervention involve? What questions were used to foster metacognition? How was the study designed and carried out? What are the implications of this work? Where can I find out more? Send us your feedback Collated digests To view/remove/add notes and save your collated digests click here Get Word Reader Understanding graphs – does metacognitive questioning help students develop and refine their mathematical ideas? This digest found in Thinking skills Mathematics Send to a friend Word doc 80KB Printer friendly Collate for later What sorts of conceptual problems did the students have? As background to the study the author described research into students' understanding of graphs, constructivist and cooperative learning, metacognitive instruction and students' "alternative conceptions" (beliefs and understandings that diverge from generally accepted models) of graphs. Some of the conceptual difficulties that students showed when interpreting or constructing graphs related to: confusing the height and the slope; putting in only one point; treating a graph as a series of point by point changes rather than as representations of a continuously changing situation; and regarding all graphs as representing positive relationships. The researcher suggests that these alternative conceptions (or misconceptions) limit students' ability to develop what she refers to as 'graph sense'. She quotes research that suggests that 'graph sense' means students looking at the entire graph, or the relevant part of it, and understanding that it expresses the overall way in which two variables change in relation to each other.