In this study, we investigated prospective secondary mathematics teachers’ development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written artifacts from these teaching sessions, and their answers to pre-and-post written assessment questions. Results point toward prospective teachers’ improved meanings regarding the definition of complex numbers and the algebraic and geometrical meanings of the Cartesian form of complex numbers. Implications for mathematics teacher education include providing specific tasks and strategies for strengthening the knowledge of prospective and in-service teachers.
Exploring Prospective Teachers’ Development of the Cartesian Form of Complex Numbers
Gülseren Karagöz Akar, Merve Saraç, and Mervenur Belin
Filling Vases and Making Tanks
Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.
Building Coherence and Progression on Sound Frameworks
Travis Lemon and Scott Hendrickson
A robust framework can support teachers and their students’ learning.
Experience First, Formalize Later
Sarah Stecher, Luke Wilcox, and Lindsey Gallas
The EFFL model empowers students to build strong conceptual understanding of mathematics through carefully designed, equity-minded activities that disrupt the traditional lecture-based classroom.
Using Series to Construct Pythagorean Triples
Darien DeWolf and Balakrishnan Viswanathan
This article provides a series-focused approach to computing Pythagorean triples.
Are We Preparing Agents of Change or Instruments of Inequity? Teaching Toward Antiracist Mathematics Teacher Education
Joel Amidon, Anne Marie Marshall, and Rebecca E. Smith
The authors began this work with the understandings that (a) there is no “neutral” when it comes to the teaching of mathematics, and (b) mathematics teacher educators need to do something to help produce teachers of mathematics that develop students’ relationships with mathematics and push against the inequities that exist both within and outside of the classrooms in which they will teach. In response, the authors created, deployed, and studied a learning module in an attempt to enact antiracist mathematics teacher education. The learning module activities, the findings about the learning from the prospective teachers who engaged in the module, and messages for mathematics teacher educators who want to engage in this work are shared.
See, Think, and Wonder Geoboard Art
Two original images were inspired by the use of an art studio app for digital drawings. This artistic process could be used to help created other original art and during See-Think-Wonder routines emphasizing meaningful observations and questioning skills.
Crack the Code
Karen Zwanch and Bridget Broome
This game teaches algebraic generalizations through differentiated play in pairs, small groups, or as a whole class and uses manipulatives to bridge numerical and algebraic thinking.
Teaching Is a Journey: What Did I Really Mean?
This department provides a space for current and past PK-12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.
My Funny (Mathematical) Valentine
Students create clever mathematical Valentine’s Day cards.