Tasks That Make Connections through Representations

Garofalo, Joe; Trinter, Christine P.

doi:10.5951/mathteacher.106.4.0302

Cited by 5 publications

(1 citation statement)

References 1 publication

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“…math symbols, computational procedures, diagrams or pictures, and verbal descriptions or arguments) that are easily tangible, visible and able to be manipulated. Yet, effective use of educational technology requires guidance and instruction by the teacher, as students rarely make the important connections on their own merely through the use of technology (Cory and Garofalo, 2011; Garofalo and Trinter, 2012). When teachers effectively use a variety of representations of mathematical and scientific concepts, students have the best chance of developing a deeper understanding of the material (Garofalo and Trinter, 2012; Goldman, 2003; NCTM, 2000; NSTA, 2003).…”

Section: Theory Of Action Regarding the Leadership Of Educational Technologymentioning

confidence: 99%

The development and impact of team-based school technology leadership

Dexter

Barton

2021

JEA

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PurposeThe authors tested the efficacy of a team-based instructional leadership intervention designed to increase middle school mathematics and science teachers' use of educational technologies for multiple representations of content to foster students' conceptual understandings. Each school's leadership team comprised an administrator, a technology instructional specialist role, and a mathematics and a science teacher leader.Design/methodology/approachThe authors tested the intervention in a quasi-experimental design with five treatment and five matched comparison schools. Participants included 48 leadership team members and 100 grade 6–8 teachers and their students. The authors analyzed data using two-level, nested multiple regressions to determine the effect of treatment on leaders' practices; leaders' practices on teachers' learning and integration; and teachers' learning and integration on students' learning. Leaders and teachers completed monthly self-reports of practices; students completed pre- and post-tests of knowledge in science and math.FindingsSignificant treatment effects at the leader, teacher and student levels establish the efficacy of this team-based approach to school leadership of an educational technology integration innovation. Leaders at treatment schools participated in a significantly higher total frequency and a wider variety of leadership activities, with large effect sizes. Teachers participated in a significantly wider variety of learning modes focused on technology integration and integrated technology significantly more frequently, with a wider variety of technologies, all with moderate effect sizes. Students in treatment schools significantly outperformed students in comparison schools in terms of science achievement but not in mathematics.Research limitations/implicationsThe overall sample size is small and the approach to participant recruitment did not allow for randomized assignment to the treatment condition. The authors tested the influence of treatment on leader practices, on teacher practices, and on student achievement. Future work is needed to identify the core components of treatment that influence practice and investigate the causal relationships between specific leaders' practices, teacher practices and student achievement.Originality/valueThis study establishes the efficacy of a replicable approach to developing team-based instructional leaders addressing educational technology. It contributes to the knowledge base about how district leaders and leadership educators might foster school leaders' instructional leadership, and more specifically technology leadership capacity.

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Section: Theory Of Action Regarding the Leadership Of Educational Technologymentioning

confidence: 99%

The development and impact of team-based school technology leadership

Dexter

Barton

2021

JEA

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Students’ Mathematical Learning Behaviour in Teaching-for-Understanding Classes: Senior High School and First-Year University Students’ Views

Velzen

2020

The Educational Forum

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Evaluating the suitability of mathematical thinking problems for senior high‐school students by including mathematical sense making and global planning

Velzen

2016

The Curriculum Journal

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To cite this article: Joke H. van Velzen (2016) Evaluating the suitability of mathematical thinking problems for senior high-school students by including mathematical sense making and global planning, The Curriculum Journal, 27:3, 313-329, DOI: 10.1080/09585176.2016 ABSTRACTThe mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an evaluation method by including mathematical sense making and global planning. Eighteen 11th-grade high-school students, divided into three groups of three pairs, solved six mathematical thinking problems that included the finding of a numeric solution and the writing of mathematical texts and arguments. Content analysis of the students' solution procedures provided for three kinds of hierarchically ordered mathematical sense-making categories. The results showed the expected statistically significant difference between the kinds of problems, though only mathematical sense making enabled the exclusion of the routine problem. The implications for practice are discussed.

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Tasks That Make Connections through Representations

Abstract: Students think resiliently about using the quadratic formula, analyzing factors graphically, finding the shortest distance between two points, and finding margin of error.

Cited by 5 publications

References 1 publication

The development and impact of team-based school technology leadership

The development and impact of team-based school technology leadership

Students’ Mathematical Learning Behaviour in Teaching-for-Understanding Classes: Senior High School and First-Year University Students’ Views

Evaluating the suitability of mathematical thinking problems for senior high‐school students by including mathematical sense making and global planning

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