Virginia Mathematics Teacher Fall 2016

them for validity and reliability. The pre-post content assessment was designed by the curriculum development team. The instrument was tested with a group of middle school mathematics teachers. Based on their responses to items and feedback on the instrument adjustments were made before the instrument was used with project participants. Interested readers may contact the authors if they would like more information about the evaluation instruments used in this project. The self–reported knowledge growth survey asked teachers to rate their understanding of rational number and proportional reasoning concepts with the descriptors None, Some, A Little, or A Lot. Self-efficacy survey questions focused on perceived changes in practice. Both surveys used a 4 choice Likert scale. Principal workshops were evaluated using feedback gathered from open-ended questions at the end of each session. With respect to the mathematics content knowledge scores on the assessment instrument

Table 1: Teacher Self- Knowledge Growth Report

Please rate your under- standing of the following topics both before this Math professional develop- ment and after Modeling fractions effective­ ly.

A little

Time point

None

Some

A lot

Before …

5.6%

27.8%

66.7%

0.0%

After …

0.0%

5.6%

0.0%

94.4%

Modeling fractional opera­ tions.

Before …

16.7%

27.8%

55.6%

0.0%

After …

0.0%

5.6%

0.0%

55.6%

Teaching students to relate fractions to decimals.

Before …

0.0%

50.0%

38.9%

11.1%

After …

0.0%

11.1%

11.1%

77.8%

Modeling decimal opera­ tions.

Before …

5.6%

44.4%

50.0%

0.0%

After …

0.0%

11.1%

55.6%

33.3%

Connecting fractions, deci­ mals and percents.

Before …

0.0%

33.3%

55.6%

11.1%

After …

0.0%

5.6%

22.2%

72.2%

Misconceptions of percents students have.

Before …

0.0%

61.1%

33.3%

5.6%

After …

0.0%

5.6%

27.8%

66.7%

Teaching ratios and propor­ tions.

Before …

5.6%

27.8%

61.1%

5.6%

After …

0.0%

5.6%

22.2%

72.2%

Teaching proportional rea­ soning.

Before …

5.6%

38.9%

50.0%

5.6%

After …

0.0%

5.6%

16.7%

77.8%

Helping students solve pro­ portional problems without computation. Developing tasks that en­ courage student discourse and engagement.

Before …

27.8%

38.9%

27.8%

5.6%

After …

0.0%

5.6%

16.7%

77.8%

Before …

5.6%

38.9%

50.0%

5.6%

After …

0.0%

11.1%

22.2%

66.7%

increased from a pre-test mean of 46.47 ( SD = 22.5) to a post-test mean of 84.61 ( SD = 20.78). Based on a paired sample t test, there was a significant difference between the pre- and post-test means ( t =-8.107, n=17, p<.01). Teachers increased their understanding of rational number and proportional reasoning concepts by completing the course. The self-reported content knowledge survey was given at the beginning and end of the summer institute (see Table 1). At the beginning of the summer institute, no one reported knowing “a lot” about how to effectively model fractions. At the completion of the workshop, 94.4% of the participants felt they could effectively model fractions. Similar trends were seen in modeling fraction operations, modeling decimal operations,

and connecting fractions, decimals, and percents. There was a 66.6% increase in the number of participants that reported knowing “a lot” about teaching ratios and proportions. Findings suggest that overall teachers believed they increased their knowledge growth by the conclusion of the summer institute. Table 2 contains data from the self-efficacy survey. In a similar manner, by the completion of the summer institute participants felt more confident about their abilities to help students understand rational number concepts. Specifically, all participants selected either “agree” or “agree strongly” to many of the statements. For example, participants responded more positively to statements like “when a student has difficulty understanding a math concept, I am confident I

Virginia Mathematics Teacher vol. 43, no. 1

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