Predicting student problem-solving strategies is a complex problem but one that can significantly impact automated instruction systems since they can adapt or personalize the system to suit the learner. While for small datasets, learning experts may be able to manually analyze data to infer student strategies, for large datasets, this approach is…

The Jeong (2020) study found that greater use of backward and depth-first processing was associated with higher scores on students' argument maps and that analysis of only the first five nodes students placed in their maps predicted map scores. This study utilized the jMAP tool and algorithms developed in the Jeong (2020) study to determine if the…

In this report we show an investigation of how high-school students learn strategies to find intermediate numbers in an interval to understand the property of numerical density. Research has shown that some high-school students have difficulty in understanding this property. To mitigate this difficulty, we proposed a Hypothetical Learning…

This paper investigates the expectations that a group of preservice secondary mathematics teachers had for how students would approach four particular algebra problems. Their responses to a set of open-ended items were content analysed. Findings show that the teachers ranged in the expectations that they held for their students. Some teachers…

Despite curriculum expectations, many students, including a disproportionate number of girls, do not 'just know' (retrieve) single-digit addition facts by Year 3. The current study employed structured interviews to explore which strategies Year 3/4 students (n = 166) used when solving more difficult addition combinations. Results revealed that…

This study invested 24 effective and 16 ineffective problem-solving kindergarten children's awareness of metacognitive self-regulated learning (MSRL) while watching other child's problem-solving behaviors. The model in a video performed a task with a trial-and-error approach and finally asked for help. After watching the video, children were asked…

One pedagogical technique that promotes conceptual understanding in mathematics learners is self-explanation integrated with worked examples (e.g., Rittle-Johnson et al., 2017). In this work, we implemented self-explanations with worked examples (correct and erroneous) in a software-based Intelligent Tutoring System (ITS) for learning algebra. We…

Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

This study investigated how motivational orientations and learning strategies predict ninth graders' non-routine mathematical problem-solving anxiety. Non-routine mathematical problem-solving anxiety classification and prediction were investigated through TwoStep cluster analysis, linear discriminant analysis, and logistic regression. 274 ninth…

Self-regulated learning (SRL) is a critical component of mathematics problem solving. Students skilled in SRL are more likely to effectively set goals, search for information, and direct their attention and cognitive process so that they align their efforts with their objectives. An influential framework for SRL, the SMART model, proposes that…

The purpose of this study was to explore students' approaches to problem identification and the effects of these approaches on problem identification, problem solving, and divergent thinking. Eighth and ninth grade students (N = 90) responded to semi-structured interview prompts while completing a creative problem-solving task (i.e., Creative…

Fluency is an important aspect of mathematics learning and plays a major role in developing proficiency as students are required to use skills and apply knowledge. This paper draws upon findings from a large project that aimed to explore primary students' mathematical fluency. Data from 160 primary students (K-6) from a NSW Departmental school…

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…

Feedback in educational technologies can teach and engage students in math, but questions remain on how to present failure feedback that supports positive learning behaviors. We explore how error- and reward-based feedback influenced students' choices to replay completed problems in "From Here to There!," a math game-based educational…

In the present study, we tested the hypotheses that: a) there are individual differences in secondary students' conceptual and procedural fraction knowledge, and b) these differences are predicted by students' approach (deep vs. surface) to mathematics learning. We used two instruments developed and evaluated for the purposes of the study which…