I want to use this occasion to reflect a bit on what the development of a consensual list of Student Learning Outcomes (SLOs) represents vis-a-vis the field of mathematics teacher education and, in particular, its curricular history. I want to suggest that GeT: A Pencil has helped the larger mathematics education community make progress in […]

Evaluate geometric arguments and approaches to solving problems. Geometry courses provide a natural setting for students to reflect on their reasoning, share their reasoning, and then critique the reasoning of their peers. If students only ever see correct arguments given by teachers and textbooks, they may not learn how to critically evaluate arguments. The ability […]

Demonstrate knowledge of the history and basics of Euclid’s Elements and its influence on math as a discipline.  Euclidean geometry is named after Euclid, the Greek mathematician who lived in Alexandria around 300 BCE. Euclid put together what was known at the time about Euclidean geometry into the thirteen books of The Elements. In The Elements, Euclid sets out […]

Be able to carry out basic Euclidean constructions and to justify their correctness. Geometric constructions support the curriculum in a GeT course and the development of mathematical thinking in several essential ways:  For these reasons, constructions remain an essential part of any GeT course curriculum. It should be noted that within the context of geometry, […]

Use transformations to explore definitions and theorems about congruence, similarity, and symmetry. Typically, there are three different approaches from which instructors can choose in order to embed transformation geometry learning outcomes into a GeT course. Instructors may choose to teach a GeT course using a formal transformation approach; they may choose to include a dedicated […]

SLO 3: Secondary Geometry Understanding. Understand the ideas underlying the typical secondary geometry curriculum well enough to explain them to their own students and use them to inform their own teaching. While there are students who do not plan to teach geometry in Geometry for Teachers (GeT) courses at most institutions, it is required for […]

SLO #5  [Definitions] Understand the role of definitions in mathematical discourse: The role of definitions in mathematics is a rich area for students’ exploration that is often overlooked. In many math classes, definitions are given by the textbook or teacher. However, in a geometry class, definitions can be a fruitful area for students to explore. Students […]

SLO 9: Non-Euclidean Geometries.  Compare Euclidean geometry to other geometries such as hyperbolic or spherical geometry. Just as visiting another country can offer us a richer perspective on our own culture, so too can the study of non-Euclidean geometries help students to develop a deeper understanding of Euclidean geometry. While it is natural for students to be […]

“One must be able to say at all times – instead of points, straight lines, and planes – tables, chairs, and beer mugs. “David Hilbert [4] Axioms serve as fundamental bricks in the foundations of mathematics. Given a small collection of statements assumed to be true, a universe of subsequent truths may spring forth, grounded in […]

During the 2019-2020 academic year, the Teaching GeT working group developed a set of Student Learning Objectives (SLOs) for the GeT courses. This year, the working group is still focused on the SLOs. We are working on writing narratives elaborating on each SLO. An example draft narrative for one of the SLOs, SLO 4 on […]