Problematizing the familiar in Ghana: Can in-service training on authentic problem-solving help teachers construct deeper understandings of new mathematics instructional models?

• In Event: Partnering with the Global South: Why Early Numeracy Skills Deserve an Equal Role in Early Grade Literacy Interventions - Part I

Proposal

This presentation looks at the extent to which a pilot in-service program that challenged Ghanaian teachers’ beliefs about mathematics helped them understand and adopt new instructional models.
The theoretical framework is based on Schoenfeld’s theory of teaching (1998, 1999, 2008) that postulates that teachers’ classroom decision making is rooted in their knowledge and beliefs. In the case of early primary mathematics, what teachers teach and how they teach is linked to what they believe mathematics to be and how they believe it should be taught. In the case of Ghanaian primary teachers, these beliefs are largely mechanistic and procedural: they believe that mathematics consists of facts and procedures to be memorized and the best way to achieve this is through explicit, teacher-led instruction (School to School, 2016). Unfortunately, the definition of mathematics and the related instructional models that underpin the mathematics reform movement (see NCTM 2014; Spangler and Wanko, 2017) do not align these beliefs. This is problematic. An increasing body of evidence suggests that teachers filter new instructional models through existing, albeit tacitly held, belief structures: when the proposed models do not align with these belief structures, teacher either reject them outright or re-interpret them (Ernest, 1999; Hersh, 1986; Jurdak 1991; Schoenfeld 2002, Arcavi & Schoenfeld 2008; Speer 2005; Hollingsworth 1989, Mumby 1982, Richardson 1986). The result is classroom instructional practices that bear little resemble to the reform models presented.
The above suggests that if teachers are to adopt with any degree of fidelity new mathematics instructional models, they need to modify their beliefs about what mathematics is and how it should be taught. Arcavi and Schoenfeld (2008) suggests that one means of doing this is to use the unfamiliar to problematize the familiar - to immerse teachers in authentic math problem solving activities (or have them analyse instructional videos) where both the mathematics and how it is taught bear little resemblance to the mathematics teachers learned in primary school, or to how they learned it. Engaging in reflective dialogue around such experiences can be a powerful catalyst for restructuring beliefs and increasing teachers’ willingness to adopt new instructional models. The Ghana Learning initiative tested this hypothesis in 20 pilot schools in the 2016-2017 school year.
Four different methods were used to collect data on the impact of problem-based inservice program:
1. structured interviews
2. classroom observations
3. end-of-year questionnaires
4. baseline and end-line P1 and P2 mathematics assessments

The program deepened teachers’ conceptual understanding of mathematics and changed their view of what mathematics is and how it should be taught. Teachers gradually adopted new instructional models in their classrooms. More importantly, pupils demonstrated significant learning gains in conceptual understanding, procedural fluency and mathematical reasoning.
The study proposes a means of shifting counterproductive epistemological beliefs that impede the uptake of new instructional models.

Authors

• Norma Evans, Evans and Associates

• Emmanuel Acquaye, Consultant