Disciplinary Content Knowledge

Students’ difficulties with contrapositive reasoning are well documented. Lack of intuition about contrapositive reasoning and lack of a meta-argument for the logical equivalence between a conditional claim and its contrapositive may contribute to students’ struggles. This case study investigated the effectiveness of the eliminating counterexamples intervention in improving students’ ability to construct, critique, and validate contrapositive arguments in a U.S. eighth-grade mathematics classroom.

Science teachers must sometimes teach outside of their expertise, and this type of teaching assignment is referred to as being out-of-field. Among newly hired teachers, this type of assignment may have a detrimental impact in the development of their instruction. This study explored the classroom instruction of 17 newly hired teachers who were teaching both in-field and out-of-field in the physical sciences during their first three years.

Beyond initial college preparation, secondary teachers in the United States have few professional opportunities to do and learn challenging mathematics, especially incollaboration with colleagues. The Mathematics Immersion for Secondary Teachers at Scale program engages sets of teachers in local school sites, connected synchronously and asynchronously to colleagues in other sites, in doing mathematics designed to promote experiences of mathematical immersion, community, and connection to the work of teaching.

What ideas do students have about small particles of matter? The Two Cups of Liquid task is intended to elicit preservice teachers’ CKT related to students’ ideas about the small particle model (SPM) for matter. The first part of the task asks preservice teachers to articulate their own understanding about why two cups containing different volumes of liquid might have the same mass, while the second examines how elementary students might respond.

What ideas do students have about small particles of matter? The Two Cups of Liquid task is intended to elicit preservice teachers’ CKT related to students’ ideas about the small particle model (SPM) for matter. The first part of the task asks preservice teachers to articulate their own understanding about why two cups containing different volumes of liquid might have the same mass, while the second examines how elementary students might respond.

What does it mean to help students develop a small particle model of matter? The Mystery Bubble task is intended to elicit preservice teachers’ CKT related to students’ ideas about the small particle model (SPM) for matter, particularly the idea of empty space between the particles. The task presents a phenomenon in which combining ethanol and water results in a mixture that occupies less space than the combined volume of each.

What does it mean to help students develop a small particle model of matter? The Mystery Bubble task is intended to elicit preservice teachers’ CKT related to students’ ideas about the small particle model (SPM) for matter, particularly the idea of empty space between the particles. The task presents a phenomenon in which combining ethanol and water results in a mixture that occupies less space than the combined volume of each.

What is a scientific explanation and how can we support students in explaining changes in matter? The Fizzy Antacid task is intended to elicit and develop preservice teachers’ CKT related to students’ scientific explanations of changes in matter. The first part of the task asks preservice teachers to develop their own explanations and engage in scientific argumentation, while considering how elementary students might explain the Fizzy Antacid phenomenon.

What is a scientific explanation and how can we support students in explaining changes in matter? The Fizzy Antacid task is intended to elicit and develop preservice teachers’ CKT related to students’ scientific explanations of changes in matter. The first part of the task asks preservice teachers to develop their own explanations and engage in scientific argumentation, while considering how elementary students might explain the Fizzy Antacid phenomenon.