# High School Teachers’ Problem Solving Activities to Review and Extend Their Mathematical and Didactical Knowledge

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight Manuel Santos-Trigo & Fernando Barrera-Mora (2011) High School Teachers’ Problem Solving Activities to Review and Extend Their Mathematical and Didactical Knowledge, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21:8, 699-718, DOI: 10.1080/10511971003600965

Here’s the abstract:

The study documents the extent to which high school teachers reflect on their need to revise and extend their mathematical and practicing knowledge. In this context, teachers worked on a set of tasks as a part of an inquiring community that promoted the use of different computational tools in problem solving approaches. Results indicated that the teachers recognized that the use of the Cabri-Geometry software to construct dynamic representations of the problems became useful, not only to make sense of the problems statement, but also to identify and explore a set of mathematical relations. In addition, the use of other tools like hand-held calculators and spreadsheets offered them the opportunity to examine, contrast, and extend visual and graphic results to algebraic approaches.

# Helping Mathematics Students Survive the Post-Calculus Transition

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight Michael J. Cullinane (2011) Helping Mathematics Students Survive the Post-Calculus Transition, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21:8, 669-684, DOI:10.1080/10511971003692830

Here’s the abstract:

Many mathematics students have difficulty making the transition from procedurally oriented courses such as calculus to the more conceptually oriented courses in which they subsequently enroll. What are some of the key “stumbling blocks” for students as they attempt to make this transition? How do differences in faculty expectations for students and student expectations for themselves contribute to the “transition dilemma?” What might faculty incorporate into students’ learning experiences during the transition to help students better navigate the shift from procedural to conceptual, from concrete to abstract? This article offers some lessons learned in connection with these questions.

# Vertically Integrating Professional Skills Throughout A Mathematics Major

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight “Vertically Integrating Professional Skills Throughout A Mathematics Major,” by Clarice Dziak, Brian Leventhal, Aaron Luttman, and Joseph Skufca. Here’s the abstract:

In response to a university mandate to include “professional issues” as a component of every major, we have developed a vertically integrated approach to incorporating the study of professional skills and issues into the mathematics curriculum. Beginning in the first year of study, mathematics majors take an inquiry-based course in mathematical modeling using software packages that are important in business and industry, such as Excel®, Maple®, and Matlab®. In the third year, students choose between a seminar course covering topics in teaching and another covering topics related to research and work in industry. The courses are designed to introduce students to the different cultures and issues of business, industry, and teaching. Beyond these two courses, students are required to demonstrate proficiency in three core areas through a required “professional experience,” which takes the form of an internship, undergraduate research experience, or educational outreach program.

Full reference:Clarice Dziak, Brian Leventhal, Aaron Luttman & Joseph Skufca (2014) Vertically Integrating Professional Skills Throughout A Mathematics Major, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 24:4,301-308, DOI:10.1080/10511970.2013.876472

# Gamification and Web-based Homework

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight “Gamification and Web-based Homework,” by Geoff Goehle. Here’s the abstract:

In this paper we demonstrate how video game mechanics can be used to help improve student engagement with online mathematics homework. Specifically, we integrate two common video game systems, levels and achievements, with the online homework program WeBWorK. We describe the key features of the implementation of these systems and discuss how students responded after they were used in a calculus class.

Full reference: Geoff Goehle (2013) Gamification and Web-based Homework, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 23:3, 234-246, DOI: 10.1080/10511970.2012.736451

# Influences of Teaching Approaches and Class Size on Undergraduate Mathematical Learning

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight Jo Clay Olson , Sandy Cooper & Tom Lougheed (2011) Influences of Teaching Approaches and Class Size on Undergraduate Mathematical Learning, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21:8, 732-751, DOI: 10.1080/10511971003699694

Here’s the abstract:

An issue for many mathematics departments is the success rate of precalculus students. In an effort to increase the success rate, this quantitative study investigated how class size and teaching approach influenced student achievement and students’ attitudes towards learning mathematics. Students’ achievement and their attitudes toward learning mathematics were compared across four treatments of a precalculus course. The four treatments were (a) traditional lecture-based structure, (b) traditional lecture-based structure with a reduced class size, (c) instruction that engaged students in problem solving, and (d) instruction that included opportunities for small collaborative groups. The achievement of students engaged in problem-based learning (PBL) was significantly higher than the other treatments. These findings suggest that undergraduates benefit from instruction that encourages reflection on prior knowledge while developing new ideas through problem solving. Surprisingly, students in the PBE treatment did not continue to outperform students in the other treatments in calculus. These findings suggest the need for longitudinal studies that investigate the long-term effect of teaching approach and small class size on student learning and student success in advanced mathematics courses.

# Improvisation in the Mathematics Classroom

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight “Improvisation in the Mathematics Classroom” by Andrea Young. Here’s the abstract:

This article discusses ways in which improvisational comedy games and exercises can be used in college mathematics classrooms to obtain a democratic and supportive environment for students. Using improv can help students learn to think creatively, take risks, support classmates, and solve problems. Both theoretical and practical applications are presented.

Full reference: Andrea Young (2013) Improvisation in the Mathematics Classroom, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 23:5, 467-476, DOI: 10.1080/10511970.2012.754809

# An Evaluative Calculus Project: Applying Bloom’s Taxonomy to the Calculus Classroom

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight Gizem Karaali (2011) An Evaluative Calculus Project: Applying Bloom’s Taxonomy to the Calculus Classroom, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21:8, 719-731, DOI: 10.1080/10511971003663971

Here’s the abstract:

In education theory, Bloom’s taxonomy is a well-known paradigm to describe domains of learning and levels of competency. In this article I propose a calculus capstone project that is meant to utilize the sixth and arguably the highest level in the cognitive domain, according to Bloom et al.: evaluation. Although one may assume that mathematics is a value-free discipline, and thus the mathematics classroom should be exempt from focusing on the evaluative aspect of higher-level cognitive processing, I surmise that we as mathematics instructors should consider incorporating such components into our courses. The article also includes a brief summary of my observations and a discussion of my experience during the Fall 2008 semester, when I used the project described here in my Calculus I course.

# Hands on SET

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight “Hands-on SET®,” by Hannah Gordon, Rebecca Gordon, and Elizabeth McMahon. Here’s the abstract:

SET® is a fun, fast-paced game that contains a surprising amount of mathematics. We will look in particular at hands-on activities in combinatorics and probability, finite geometry, and linear algebra for students at various levels. We also include a fun extension to the game that illustrates some of the power of thinking mathematically about the game.

Full reference: Hannah Gordon, Rebecca Gordon & Elizabeth McMahon (2013) Hands-on SET®, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 23:7, 646-658, DOI: 10.1080/10511970.2013.764368

# Creating a Culture of Inquiry in Mathematics Programs

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight “Creating a Culture of Inquiry in Mathematics Programs,” by Jill Dietz. Here’s the abstract:

We argue that student research skills in mathematics should be honed throughout the curriculum just as such skills are built over time in the natural and physical sciences. Examples used in the mathematics program at St. Olaf College are given.