Careless Errors Made by Sixth-Grade Children on Written Mathematical Tasks

Abstract

An investigation into mathematical errors made by 50 sixth-grade children attending an international primary school in Lae, Papua New Guinea, is described. The children were given a battery of tests, with one of the tests, the Monash Assessment of Mathematical Performance (MAMP), being administered twice. Errors made by the children on either, or both, occasions they did the MAMP test were analyzed by means of the Newman interview technique. Attention was focused on errors made on one occasion but not on the other: An error of this type was deemed to have been ”careless” if a child confidently demonstrated, to the interviewer, that he or she knew how to obtain the correct answer to the question and if neither the child nor the interviewer could identify why the original error had been made. Of all the errors made by the children on MAMP questions, 21% were in this category. Analysis revealed that the proportion of careless errors correlated significantly and positively with measures of arithmetical competence, mathematical language, and mathematical confidence but negatively with a measure of misplaced confidence.

Finding Rigor Within a Large-Scale Expansion of Preschool to Test Impacts of a Professional Development Program

“…Furthermore, a previous study of BB found that mathematical classroom culture mediated the relationship between the intervention's receipt with child outcomes . This is consistent with the literature supporting the connection between academic performance and general classroom features, including signs of mathematical activity, teachers who are knowledgeable and enthusiastic about mathematics, and teachers who frequently interact and respond to children (Clarke & Clarke, 2004;Clements & Sarama, 2007).…”

“…That is, teachers in wellorganized classrooms that provide a structured environment where expectations and routines were delineated were able to implement more math activities (Bulotsky-Shearer et al, 2014). The BB curriculum is structured around weekly lesson plans consisting of four main instructional components: Whole Group, Small Group, Hands-On Math Centers, and Computer (Clements & Sarama, 2007). A higher degree of classroom organization, likely, facilitated teachers' ability to set up and implement multiple BB components throughout the preschool day.…”

“…The curricular materials include an evidence-based math curriculum called Building Blocks (BB; Sarama et al, 2008) and a research-based Pre-K for All (PKA) Interdisciplinary Units of Study (Units 1 ) developed by the Division of Early Childhood Education at New York's Department of Education (DECE-DOE). The decision to create a PD track that incorporated a math-focused curriculum was based on evidence that (1) preschool children's math skills are foundational for a broader set of outcomes, including language, reading, and executive function (e.g., Duncan et al, 2007;Watts et al, 2014); (2) preschool math instruction is likely minimal-in terms of the dosage of math instruction and the quality of instruction (Ginsburg et al, 2008); and (3) preschool children's math competencies can increase by training teachers using an evidencebased curriculum with supports (Clements & Sarama, 2007;Presser et al, 2012). Furthermore, because a researcher-led efficacy study of BB called Making Pre-K Count (MPC) in New York City (NYC) took place a few years earlier, there was increased interest in expanding to more sites.…”

“…Potentially, teachers who were more attuned to their children's needs were able to create a classroom that made math fun and to engage children in math activities positively. Improving the mathematical classroom culture is vital because it represents not adherence to the curriculum but rather the development of an environment that infuses math at every opportunity (Clements & Sarama, 2007). Implications for these moderation findings suggest that teachers with higher emotional support and classroom organization are better equipped to implement a math-specific PD program.…”

Incorporating Features Learned by an Enhanced Deep Knowledge Tracing Model for STEM/Non-STEM Job Prediction

“…Therefore, it is easier for them to discover interest in the STEM field which profoundly involves mathematics. As for the reason why "Ave-Carelessness" becomes a discriminating variable in the ttest, it might be attributed to the phenomena that sloppiness in tackling problems is more common in academically outstanding students [4]. In contrast, "AveResBored" and "AveResConf" are less effective in discriminating STEM and non-STEM students.…”