Research Report #11

"I need to measure the base and the height": Examining Preservice Teacher's Responses Top Area Conservation Tasks

DaeHong, University of Iowa

Abstract

purpose of this work was to explore how elementary preservice teachers respondedto area conservation tasks. We administered written pre-assessments, followedby semi-structured interviews with 23 preservice teachers, asking them torespond to and reason with area conservation tasks. Findings highlighted severalinteresting preservice teachers' challenges when assessing area conservation tasks. Inmany cases, preservice teachers exhibited struggles similar to students, especiallywith regards to the justification of their area conservation claims and they have concept images of different shapes that do not coincide with the corresponding mathematical definitions.

Exploring PSTS' Responses to Students' Volume Misconceptions

DaeHong, University of Iowa

Abstract

The purpose of this study was to explore how elementary pre-service teachersresponded to students’ hypothetical misconceptions about volume measurement. Wecarried out both pre-assessments and follow-up interviews with 17 pre-serviceteachers, with tasks focused on both volume content knowledge and hypotheticalstudent responses to volume tasks. Preliminary findings indicated a preferencetowards show-and-tell responses, often with a focus correct or incorrect use of thevolume formula. While PSTs were frequently able to correctly identify students’learning challenges with regards to volume, theyexperienced difficulty in addressingthose challenges in meaningful ways. Recommendations for supporting pre-serviceteachers in teacher education programs are discussed.

Student Gesture & Diagram Use as Assessment Data for Units Understanding

Cathy Kaduk, North Central College

Abstract

Gesture and diagram-use observations can play a role in triangulating evidence when making short-term decisions about students’ thinking. Results of an analysis of fourth-grade students solving array multiplication problems provide data for making inferences about student number construction (units understanding) and related inferences about additive vs multiplicative reasoning by using gestures, verbal thinking, diagram-use, and other written work. Array multiplication problems are common in third –sixth grade. Break-apart multiplication examples in the study represent the distributive property. The analysis of video and written work from 64 protocol interviews of students’ gestures, explanations, and written work using a coding system based on prior unit coordination studies led to the development of a teacher observational tool for this purpose. Training teachers and teacher candidates to observe gestures and diagram use is underway.

Jan 27, 2022 07:00 PM : Becoming a Teacher of Mathematical Modeling, Grades 6–12

As we think about our role in education, we take to heart our responsibility to use education to leave the world better than we found it. In our work, we have come to realize that mathematical modeling inherently provides opportunities for access, equity, and empowerment for every student, and we see in teaching mathematical modeling the opportunity to teach empathetic critical thinking skills. Modeling is a way for students—human beings—to use their mathematical skills in examining different solutions to authentic problems based on different perspectives. Because students bring their own knowledge and perspectives to a modeling problem, it is likely that the modeling process will unfold in different ways for different problems. To help navigate this complexity, we ground our conceptualization of modeling in four big ideas that underpin the classroom practice of mathematical modeling. In this session, we will discuss these four big ideas and explore examples of how they play out in grade 6-12 classroom settings, focusing on how empathy, as a practice, can and should be cultivated in students’ mathematical modeling.