Bibliographic record
Abstract
Thoughts on Teaching and Learning Mathematics Toronto, Ontario: Queen's Printer for Ontario, 2015, 4 hours ISBN: 978-1-4606-6609-8 (DVD) Thoughts on Teaching and Learning Mathematics is a video compilation of interviews of education experts recorded during the 2015 Ontario Association for Mathematics Education (OAME) conference. The resource is aimed at mathematics educators at the elementary and secondary school levels. The topics resonate with current issues in mathematics classrooms throughout Ontario and are explained by individuals who are well respected by mathematics educators in the province. Unfortunately, although the individuals who were interviewed cite a few pieces of research, the resource as a whole is not heavily research-based. LearnTeachLead attempted to section the resource into small, usable sections consisting of 5- to 10-minute video clips; in actuality, however, the resource is dissected in such a way that it is hard to follow or to extract meaningful content. Interview questions were not asked on video, meaning that the viewer needs to remember the title of the segment to understand the subject under discussion. While the closed captioning helps slightly with comprehension, the resource overall is not an effective means of communicating about the issues. The DVD is available on the LearnTeachLead website (http:// learnteachlead.ca/project_category/mathematics/). Full transcripts of the interviews have been published online and are a slightly more effective choice of media for this resource. The first segment addresses mathematical thinking for every learner. In this segment, Chris Suurtamm speaks of what she thinks are the causes of mathematics anxiety and how to overcome it. She challenges teachers to think of different ways in which students think about problems, different ways to solve them and to accept the possibility that teachers themselves do not always have all the answers. She invites teachers to involve parents in students' mathematical learning, to help change the society's perspective of mathematics learning, and to look at the curriculum for what the students should be doing in the classroom. Suurtamm also stresses the importance of having teachers deepen their understanding of mathematics knowledge for teaching through collaborating with their colleagues. She also argues that sound assessment is ongoing assessment in which teachers are listening and responding to how students are thinking. She stresses that students need to receive feedback as to how they are doing, as opposed to just a mark. Nora Newcombe presents the second segment, which addresses spatial reasoning. Newcombe defines spatial reasoning and provides examples of how certain mathematics principles can be thought of spatially. The concepts she mentions are shapes, the equals sign, and the continuous number line. Pedagogically speaking, she believes direct instruction and play-based learning should be used together. On the topic of gender, Newcombe speaks briefly about her belief that the scientific community should realize that both girls and boys can be engaged and can improve their special reasoning skills. Educators should therefore simply dedicate themselves to learning and not to figuring out the gender differences. Finally, Newcombe describes some research she has completed with preschoolers. Her research suggests that although digital manipulatives may be useful, physical manipulatives led to better conversations about the shapes and therefore may be more useful for learning. Marian Small begins her interview about substantive mathematics learning by saying that it makes sense to use games to help kids learn automaticity. Casual learning makes learning fun and inviting. She believes that it is important to have good mental mathematics skills and that the development of good mental mathematics skills should be part of the goal of mathematics educators. On mathematics anxiety, she believes that students pick up anxiety from teachers and parents. …
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.005 | 0.009 |
| Scholarly communication | 0.005 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.031 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".