The ability to do math provides students with an important tool for understanding the world and solving real-life problems. However, many students experience anxiety when encountering math and may avoid learning arithmetic (Guilford 1980). This can lead to a lack of academic achievement and life success. Research has shown that reducing students’ mathematics anxiety and promoting their learning self-efficacy, motivation, and interest can improve their performance (Peters 2013).
Effective teaching of arithmetic involves establishing clear goals for the mathematical knowledge and skills to be learned, situating those goals within a learning progression, and using the goals to guide instructional decisions. Additionally, instruction should involve the use of a variety of mathematical representations and provide opportunities for students to connect those representations to deepen their understanding and solve problem-solving tasks.
Research has found that arithmetic fluency is closely related to working memory (WM) and inhibitory control (the ability to delay gratification). A number of studies have found that when a child has poor WM and inhibitory control, they also have difficulty with basic arithmetic. To address this, several researchers have developed and tested arithmetic interventions designed to teach children these skills. The results of these interventions are promising, but the effect sizes are typically small and it is difficult to determine whether the intervention had a meaningful impact on arithmetic proficiency.
It is possible that the reason a number of interventions have failed to produce significant effects is because they do not focus on building working memory and inhibitory control, or because they are too short in duration. However, the fact that many different intervention studies have been conducted in primary schools and tertiary institutions makes it challenging to compare their findings. Finally, the intervention methods used in these studies may vary significantly, which could also influence their effectiveness.
The most effective arithmetic interventions have demonstrated the capacity to help students make sense of mathematical information and construct viable arguments. This can be accomplished by using stated assumptions, definitions, and previously established results to support and strengthen a hypothesis or position. Mathematically proficient students can also assess the strength of another argument and respond to counterexamples.
In order to increase their mathematics self-efficacy, students must be able to interpret and evaluate their intermediate outcomes. Moreover, they must be able to use the outcome of an experiment or task to inform their current beliefs about their competence in the subject. For example, if a student accomplishes a difficult task successfully, this can elevate their judgement of their own competence, while a failure can lower it.
One way to promote mathematics self-efficacy is to integrate the four self-efficacy features – anxiety coping strategy, modeling example (vicarious experience), mental practice, and effort feedback – into a computerized example-based learning activity. For example, Ramdass and Zimmerman (2008) report that an intervention that combines these strategies improved student mathematics self-efficacy. The findings of this study are promising, but further experimental work is needed to understand the underlying mechanism.