A Little Change Can Make a Big Difference

The opportunity to teach mathematics through service learning projects provides a relevant and connected experience that encourages concept development and problem solving proficiency while also developing students’ feelings of generosity and altruism. In this article I describe a prior project that helped my students, many of whom struggled with mathematics, become engaged in mathematical thinking and reasoning. Additional specific connections are made toward extended projects surrounding current events, as well as state and national standards

Seeing Mathematics Through Different Eyes: An Equitable Approach to Use with Prospective Teachers

Teacher educators need to prepare prospective teachers by encouraging them to critically examine their current beliefs about the teaching and learning of mathematics while also providing opportunities for prospective teachers to develop an equity-centered orientation. Attending to these practices in teacher preparation programs may help prospective teachers observe actions that occur in classrooms and determine effective strategies that provide the opportunity to enhance all students’ access to high-quality mathematics instruction. As mathematics teacher educators, we must recognize what prospective teachers attend to as they direct their attention to various classroom events and how they relate the events to broader principles of teaching and learning. In this chapter, we investigate what prospective teachers attend to in a classroom vignette of a student who is above grade level in mathematics and exhibits disruptive behavior during instruction. Keeping everything constant in the vignette except the student’s race and sex, we examined prospective teachers’ responses when the student was an African American male, White male, African American female, and White female. By attending specifically to race and sex, we explored whether prospective teachers demonstrated (1) an equity-centered orientation toward mathematics instruction or (2) deficit views of students based on race, sex, or the intersection of the two. Using a constant comparative method, the data were coded and analyzed using the equity noticing framework. The results indicate that prospective teachers are beginning to attend to cultural influences and their responses reveal differences not only between races but also between males and female

Maths Games: A Universal Design approach to mathematical reasoning

By incorporating math games into the classroom, through the principles of Universal Design teachers are able to address mathematical content, reasoning and problem solving, as well as tailoring games to address students\u27 individual needs

What, how, who: Developing Mathematical Discourse

A collaborative classroom, an open-ended problem, and a what-how-who structure can build students’ reasoning skills and allow teachers to recognize all classroom contributions. With an increased focus on using social discourse to enhance students’ mathematical thinking and reasoning (NCTM 2014, Staples and King 2017), teachers are looking for discussion strategies that encourage middlelevel students to make sense of mathematical concepts. However, structuring these valuable discussions is complex. “Mathematical discourse should build on and honor student thinking, and provide students with opportunities to share ideas, clarify understandings, develop convincing arguments, and advance the mathematical learning of the entire class” (Smith, Steele, and Raith 2017, p. 123). In other words, teachers must carefully consider what tasks provide meaningful opportunities to explore ideas, generate hypotheses, and promote questions within a collaborative environment. Then, teachers need to consider how to structure the activity to encourage discussions and incorporate responses that contribute to understanding specific mathematical objectives. Additionally, teachers must select who will speak to “advance the mathematical storyline of the lesson” (NCTM 2014, p. 30). By intentionally focusing on these elements in mathematics instruction, middle-grades teachers can develop a classroom culture that not only emphasizes sense making but also values the intellectual capacity that students bring to the classroom (Gutiérrez 2013; Lemons-Smith 2008). In this article, we describe how teachers can promote meaningful discussions using the what-how-who structure while giving students opportunities to make sense of mathematical ideas within a social context

Sliding into an equitable lesson

A kindergarten teacher uses Gutierrez\u27s four dimensions of equity to design and facilitate geometry instruction. Equitable instruction is reflected in how students are positioned in the classroom and how their identities evolve through purposeful interactions that value and recognize the intellectual capacity of each student (Gutiérrez 2013; Lemons-Smith 2008). These integral interactions occur when teachers and students exchange problem-solving strategies, discuss relations among various mathematical representations, and listen to the viewpoints of others (NCTM 2000; 2014)

Multiple perspectives on cognitive development: Radical constructivism, cognitive constructivism, sociocultural theory, and critical theory

This multi-vocal article represents the work of three teacher educators. In conjunction with Glasersfeld’s (1996) description of Radical Constructivism, we agree that any theory “cannot claim to be anything but one approach to the age-old problem of knowing. Only its application in contexts where a theory of knowing makes a difference can show whether or not it can be considered a viable approach.” (von Glasersfeld, 1996, p. 309). In this conceptual piece, we examined the relationship between Radical Constructivism and three distinct, yet sometimes overlapping, theories: 1) Cognitive Constructivism 2) Sociocultural Theory; and 3) Critical Theory. First, we discuss the key premises, elements, and/or assumptions of each theory as well as points of convergence and divergence between each theory and Radical Constructivism. Secondly, we will analyze the opening vignette through the three different theoretical lenses

A Little Change Can Make a Big Difference

The opportunity to teach mathematics through service learning projects provides a relevant and connected experience that encourages concept development and problem solving proficiency while also developing students’ feelings of generosity and altruism. In this article I describe a prior project that helped my students, many of whom struggled with mathematics, become engaged in mathematical thinking and reasoning. Additional specific connections are made toward extended projects surrounding current events, as well as state and national standards

Tools to support mathematical precision through meaningful connections.

As they move about their environments, young children have opportunities to reinforce their relational understanding and build mathematical vocabulary. Coding activities can provide opportunities to extend content explorations and provide meaningful connections among mathematical ideas, early literacy skills, and geography. Cubetto, the hands-on coding robot, was integral in Ms. Megan’s preschool classroom. Recognizing her children’s excitement, she used the robot to create collaborative, problem-solving experiences where the children explored spatial relations and used mathematical vocabulary to describe positions in space, “Cubetto is far away from the mountain” or “We need to make Cubetto go around the river—he can’t go through it!” As they navigated the obstacles, Megan fostered her preschoolers’ rational counting and number sense. She encouraged children to evaluate proposed ideas and justify their thinking as they debated how many tiles to use in order to move Cubetto from Point A to Point B: “No. We need to have four green tiles. He has to go forward four spaces, see? One, Two, Three, Four. Not five. You don’t need a green for the turn. You need a different color to turn.

A program for success: A reflective structure to enrich preschool children’s mathematical reasoning.

Innovative technology, such as coding tools, can build problem solving skills; and in recent years, coding seems to have emerged as the new “hot item” in education. Although tangible coding tools for young learners may offer several mathematical opportunities, neither the tools nor the gamelike situations guarantee children’s mathematical development. Furthermore, many teachers face challenges in effectively integrating technology within early mathematics. The Program for Success (P4S) project was designed to provide prospective preschool (ages 3 – 5) teachers’ (PTs) explicit pedagogical support during their 8-week student teaching practicum, which would enrich their proficiency integrating technology with tasks that promote preschool children’s problem solving, mathematical reasoning, and communication

Maths Games: A Universal Design approach to mathematical reasoning

By incorporating math games into the classroom, through the principles of Universal Design teachers are able to address mathematical content, reasoning and problem solving, as well as tailoring games to address students\u27 individual needs