Geometry

Speak Up or Stay Silent: How Does Teachers’ Verbal Participation in a Professional Development Programme Relate to Instructional Outcomes?

Cadre-Admin — Mon, 30 Jun 2025 18:07:03 +0000

Speak Up or Stay Silent: How Does Teachers’ Verbal Participation in a Professional Development Programme Relate to Instructional Outcomes?

Like classrooms, professional development (PD) workshops can be organised as dialogic and inclusive spaces, where the verbal contributions of the participants are critical for driving the inquiry and meeting the intended learning goals. Also, similar to how students interact during instruction, teachers’ verbal contributions during workshops may be uneven in their frequency and focus, with some individuals speaking up on particular topics, while others remain relatively silent. This study examines the nature and variation of teachers’ verbal participation during whole-group discussions as part of a weeklong mathematics PD programme. We analysed individual teachers’ talk over time and the relationship between their verbal participation and subsequent changes in their instructional practice over a two year period. The results suggest that by taking part in workshops where there were frequent, in-depth conversations focused on teaching and learning, even the quiet teachers appeared to be active listeners whose instruction was impacted by the PD. However, the mathematics lessons of their more vocal colleagues showed even more improvement, especially one year post PD. This study offers new insights regarding teacher participation when endeavouring to create equitable, discourse-rich professional learning opportunities that promote instructional growth.

Wang, C. & Jacobs, J. (2024). Speak up or stay silent: How does teachers’ verbal participation in a professional development programme relate to instructional outcomes? Professional Development in Education, 1–18. https://doi.org/10.1080/19415257.2024.2445551

Cadre-Admin Mon, 06/30/2025 - 14:07

https://www.tandfonline.com/doi/full/10.1080/19415257.2024.2445551

Examining Technology-Supported Teacher Responding and Students’ Written Mathematical Explanations

Cadre-Admin — Mon, 18 Jul 2022 20:09:53 +0000

Examining Technology-Supported Teacher Responding and Students’ Written Mathematical Explanations

This study examines technology-enhanced teacher responses and students’ written mathematical explanations to understand how to support effective teacher responding and the centering of students’ mathematical ideas. Although prior research has focused on teacher noticing and responding to students’ mathematical ideas, few studies have explored the revisions that students make to their written explanations after teacher responding and very few explore this in authentic classroom contexts. Four high school geometry teachers and thirty of their students participated in project-based tasks examining the relationships between scale factor and the dimensions, surface area, and volume of a rectangular prism. The teachers’ written feedback and the students’ written explanations were coded and scored. Results show that student explanations improved significantly after students received feedback about their mathematical ideas. Furthermore, results indicate that the teacher feedback may be more effective if it focuses on mathematical relationships between variables and that additional feedback about the variables alone may have little impact. Results contribute to an understanding of how eliciting students’ written mathematical explanations might support effective teacher responding in classroom contexts.

Bywater, J. P., Lilly, S., & Chiu, J. L. (2022). Examining technology-supported teacher responding and students’ written mathematical explanations. Journal of Mathematics Teacher Education.

Cadre-Admin Mon, 07/18/2022 - 16:09

https://link.springer.com/article/10.1007/s10857-022-09546-3

Examining Technology-Supported Teacher Responding and Students’ Written Mathematical Explanations

Cadre-Admin — Mon, 18 Jul 2022 20:09:53 +0000

Examining Technology-Supported Teacher Responding and Students’ Written Mathematical Explanations

Bywater, J. P., Lilly, S., & Chiu, J. L. (2022). Examining technology-supported teacher responding and students’ written mathematical explanations. Journal of Mathematics Teacher Education.

Cadre-Admin Mon, 07/18/2022 - 16:09

https://link.springer.com/article/10.1007/s10857-022-09546-3

Contrasting Cases in Geometry: Think Alouds with Students about Transformations

Cadre-Admin — Wed, 13 Jul 2022 15:56:11 +0000

Contrasting Cases in Geometry: Think Alouds with Students about Transformations

There is strong empirical evidence in support of learning from comparisons in mathematics education research (Rittle-Johnson & Star, 2007; Star, Pollack, et al., 2015; Star et al., 2016). Comparisons have produced gains in students’ procedural knowledge, flexibility, and conceptual knowledge of algebra (Lynch & Star, 2014; Star, Newton, et al., 2015; Star, Pollack, et al., 2015). The Animated Contrasting Cases in Geometry project seeks to extend this research and transform the learning of geometry for middle school students by designing a supplementary digital animated curriculum. The curriculum materials for each lesson are organized into Worked Example Pairs (WEPs), which include five unique features: a page for the first student’s solution strategy on a given geometry task, a page for the second student’s solution to a geometry task (which could be the same or different task as was shown on first student’s page), a page with both students’ strategies side-by-side, a discussion sheet with four questions for the students to answer, and a thought bubble page summarizing the key mathematical concepts in the problem. The discussion sheet and thought bubble page are designed to make the instructional goal of each WEP more explicit and to scaffold discussions among students as they summarize their work from the WEPs (Star, Pollack, et al., 2015). This paper focuses on the Transformations unit, which is one of four units.

Krupa, E. E., Bentley, B., & Mannix, J. P. (2021). Contrasting cases in geometry: Think alouds with students about transformations. Proceedings from the 43rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Philadelphia, PA.

Cadre-Admin Wed, 07/13/2022 - 11:56

http://www.pmena.org/pmenaproceedings/PMENA%2043%202021%20Proceedings.pdf#page=…

Animated Contrasting Cases in Geometry

Cadre-Admin — Wed, 15 Sep 2021 18:28:40 +0000

Animated Contrasting Cases in Geometry

In this collection of materials, four geometric topics are covered in animated, digital materials. There are also paper-based materials for the four geometric topics: Angles, Transformations, Pythagorean Theorem, and Volume. These topics are discussed in scenarios of contrasting cases, where two fictional students each present a unique method or solution strategy to the same problem. The goal is then to analyze both methods and discuss similarities and differences, strengths and weaknesses of each.

Cadre-Admin Wed, 09/15/2021 - 14:28

https://acinggeometry.org/

Competencies and Behaviors Observed When Students Solve Geometry Proof Problems: An Interview Study with Smartpen Technology

Cadre-Admin — Thu, 22 Apr 2021 14:56:32 +0000

Competencies and Behaviors Observed When Students Solve Geometry Proof Problems: An Interview Study with Smartpen Technology

This peer-reviewed research journal publication addresses one of the grant goals with respect to how students performed on a set of proof tasks. Student work was documented through the use of smartpen technology which allowed the researchers to "track" students' written work on the proof tasks as well as hear the students' explanations of their thinking about the tasks. Although the two tasks highlighted in this paper were relatively routine triangle congruent proofs, only 7 out of 23 of the sampled students were successful on both proofs.

Cirillo, M., & Hummer, J. (2021). Competencies and behaviors observed when students solve geometry proof problems: An interview study with smartpen technology. ZDM Mathematics Education.

Cadre-Admin Thu, 04/22/2021 - 10:56

Cirillo___Hummer_2021.pdf

https://link.springer.com/article/10.1007/s11858-021-01221-w

Engaging Students with Non-routine Geometry Proof Tasks

Cadre-Admin — Wed, 19 Aug 2020 23:55:15 +0000

Engaging Students with Non-routine Geometry Proof Tasks

Students who earned high marks during the proof semester of a geometry course were interviewed to understand what high-achieving students actually took away from the treatment of proof in geometry. The findings suggest that students had turned proving into a rote task, whereby they expected to mark a diagram and prove two triangles congruent.

Cirillo, M. (2018). Engaging students with non-routine geometry proof tasks. In P. Herbst, U. H. Cheah, P. Richard, & K. Jones (Eds.) International Perspectives on the Teaching and Learning of Geometry in Secondary Schools, (pp. 283-300). Cham, Switzerland: Springer.

Cadre-Admin Wed, 08/19/2020 - 19:55

https://link.springer.com/chapter/10.1007/978-3-319-77476-3_16

Building Mathematical Knowledge for Teaching Proof in Geometry

Cadre-Admin — Fri, 22 May 2020 02:45:42 +0000

Building Mathematical Knowledge for Teaching Proof in Geometry

Presentation slides and handout from the 2019 NCTM Regional Conference in Nashville, TN.

Cadre-Admin Thu, 05/21/2020 - 22:45

PISC_Nashville Regional.pdf

GPS Handout.pdf

CAREER: Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice

Cadre-Admin — Fri, 22 May 2020 02:37:56 +0000

CAREER: Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice

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Cadre-Admin Thu, 05/21/2020 - 22:37

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PISC Poster_CADRE_2018_Cirillo.pdf

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Linear Algebra and Geometry

Cadre-Admin — Wed, 24 Apr 2019 15:28:16 +0000

Linear Algebra and Geometry

Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.

The materials in Linear Algebra and Geometry have been used, field tested, and refined for over two decades. It is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. Secondary teachers will find the emphasis on developing effective habits of mind especially helpful. The book is written in a friendly, approachable voice and contains nearly a thousand problems.

An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.

Cadre-Admin Wed, 04/24/2019 - 11:28

https://bookstore.ams.org/text-46/