In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This…

Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

Students' previous knowledge at a superficial level is reviewed when they solve mathematical problems. This action is imperative to strengthen their knowledge and provide the right information needed to solve the problems. Furthermore, Pirie and Kieren's theory stated that the act of returning to a previous level of understanding is called folding…

How does the visual system recognize images of a novel object after a single observation despite possible variations in the viewpoint of that object relative to the observer? One possibility is comparing the image with a prototype for invariance over a relevant transformation set (e.g., translations and dilations). However, invariance over…

Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants' levels of brain activation and possible reasons for these levels as they solved…

This article discusses how 13-year-old students with above-average numeracy skills and below-average reading skills cope with comprehending word problems. Compared to other students who are proficient in numeracy and are skilled readers, these students are more disadvantaged when solving single-step and multistep arithmetic word problems. The…

This paper highlights the Indonesian's road transportation contexts, namely, angkot, that used in learning and teaching of addition and subtraction in first grade and second grade MIN-2 Palembang. PMRI approach that adopt from RME [Realistic Mathematics Education] was used in this design research. From teaching experiment was founded that the…

Gestalt psychologists proposed two distinct learning mechanisms. Associative learning occurs gradually through the repeated co-occurrence of external stimuli or memories. Insight learning occurs suddenly when people discover new relationships within their prior knowledge as a result of reasoning or problem solving processes that re-organize or…

People remember information better if they generate the information while studying rather than read the information. However, prior research has not investigated whether this generation effect extends to related but unstudied items and has not been conducted in classroom settings. We compared third graders' success on studied and unstudied…

Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7-9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __),…

Two developments have contributed to the convergence of views about the benefits of real-life and inquiry-based pedagogies in mathematics learning. First, the mathematics teaching community is increasingly focused on the learning of mathematics that involves the transfer of prior knowledge to novel problem-solving situations, a key element in…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…

Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation.…

Preschool children (n=115) in Poland were tested in five areas: counting, equipotency of sets, dividing, adding, and comparing. Results showed that these children already had informal knowledge of many of the concepts and skills included in the mathematics curriculum in the early grades. (PDD)