Constructivist Curriculum and Pedagogy as Tools for Improving Developmental Mathematics
By Erin Moss, Co-Editor, DUE Point, Millersville University
STEM graduates can have satisfying, well-paid careers in a variety of fields, yet many students turn away from those opportunities and graduate with non-STEM degrees because they believe they “can’t do math.” A unique program at the University of New Mexico at Taos implements modules designed from a constructivist perspective in developmental mathematics courses. The modules seek to increase student understanding and enjoyment of mathematics while enabling students to cultivate a growth mindset and increased employability skills. The constructivist pedagogical approach employed by the project team is based on student exploration, sense-making, peer collaboration and linking new mathematics to prior knowledge. Principal Investigator Dr. Colin Nicholls explains more about the project below.
What makes UNM-Taos an ideal place to implement this project?
As an open-access 2-year college, UNM-Taos has a large number of developmental math courses designed to prepare students for degree-level math courses. We find a significant number of students in those developmental math courses decide they ‘can’t do math’ and turn away from STEM before they’ve even experienced credit-bearing STEM courses!
What provided the inspiration for this project?
My interactions with two students in particular inspired my interest in this project. One student showed insight and creativity in math but switched into a non-STEM career because he decided that he wasn’t good at math, even though I tried to persuade him that he had the skill set to succeed.
Another student struggled mightily with mathematics. He at first thought that a mathematics student’s job was to guess which arbitrary rule to follow on a particular task. Gradually, however, he began to realize that mathematics involved sense-making and connections, and with that understanding, he began to enjoy the subject. This student went on to do postgraduate work in a STEM field.
As a result of my experiences with these students, I realized I wanted to give all students the opportunity to grasp that understanding and then let them choose for themselves whether to follow a STEM path or not, rather than believe that path wasn’t available to them.
How do you go about designing constructivist instructional modules?
Our team began by identifying the big ideas that students need to master in developmental classes that are foundational to more advanced concepts in later STEM classes and the associated learning objectives and skills. We named these big ideas “keystones.” Keystones included concepts such as proportionality, fractions, and signed integers. While there are several textbooks that develop these keystones with a constructivist pedagogy, the contexts used in the textbooks are targeted at 5th – 9th grade students. Our students are typically 19-35 years old, and thus need more sophisticated contexts.
Our activity development guru, Dr. Tom Gruszka from Western New Mexico University, uses the keystones and associated learning objectives to draft activities which are as authentic as possible while being age-appropriate for our students. As an example, for the proportionality keystone, the context used was ‘How do you make your coffee the correct strength if you don’t have enough coffee to make a whole pot?’ Tom brings each draft back to the instructional team (the Math department at UNM-Taos), and together we refine the activity. Then we work with our facilitation team, led by the Mathematically Connected Communities (MC2) group out of New Mexico State University, to define exactly how to implement the activity. We ponder questions such as: What interventions should we prepare if students get stuck at this point in the activity? How much time should we allot for students to share out to their classmates, and what format will work best? Finally, we try the activity in 2 or 3 classes, reporting back to the groups and tweaking as necessary, so that at the end, we have an activity with a defined format and facilitation notes that we can use to collect research data.
How do skills developed via constructivist pedagogy better prepare students for subsequent course-taking and/or employment?
Constructivism encourages the development of higher-level thinking and skills such as sense-making, questioning, communication, synthesis, and collaboration. All of these skills are valuable to our students in their classes and to potential future employers.
What types of research questions are you trying to answer about your project? Can you share any preliminary results?
Specifically, our research questions are: In comparison to the current textbook-based approach, will using adapted, age appropriate, constructivist math modules with associated support activities result in the following: 1) Higher student success rate? 2) Higher course completion rate? 3) Increased student ability to apply current knowledge to new applications? 4) An increase in the number of declared pre-science majors persisting into credit-bearing STEM courses?
The research phase of the program begins Fall 2021. One of the things we have already realized is that our original definition of what constituted a keystone task was too narrow and content-focused. In addition to math content keystones, we have found we need to include an icebreaker keystone (to develop the trust essential for small-group learning) and a reflection/metacognition keystone (to get students to consider the results and benefits their efforts produced, rather than just what grade they received).
Fig 1: The constructivist approach we use emphasizes small group collaboration in order to build understanding through exploration, inquiry, and sense-making, and to aid student communication and group-work skills.
Fig 2: Published research, along with Instructor experience at UNM-Taos, has shown increased student engagement and learning by moving away from conducting group-work at tables as shown in Fig 1, to having the groups conduct their work at vertical whiteboards as shown here.
Learn more about NSF DUE 1928720
Full Project Name: Using Targeted Constructivist Instructional Modules to Increase Undergraduate Students' Confidence, Knowledge, and Skills in Mathematics
Abstract: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1928720&HistoricalAwards=false
Project Contact: Dr. Colin Nicholls, PI; colnic@unm.edu
*Responses in this blog were edited for length and clarity.