Abbey M. Loehr

The Influence of Relational Knowledge and Executive Function on Preschoolers’ Repeating Pattern Knowledge

Children’s knowledge of repeating patterns (e.g., ABBABB) is a central component of early mathematics, but the developmental mechanisms underlying this knowledge are currently unknown. We sought clarity on the importance of relational knowledge and executive function (EF) to preschoolers’ understanding of repeating patterns. One hundred twenty-four children aged 4 to 5 years old were administered a relational knowledge task, 3 EF tasks (working memory, inhibition, set shifting), and a repeating pattern assessment before and after a brief pattern intervention. Relational knowledge, working memory, and set shifting predicted preschoolers’ initial pattern knowledge. Working memory also predicted improvements in pattern knowledge after instruction. The findings indicated that greater EF ability was beneficial to preschoolers’ repeating pattern knowledge and that working-memory capacity played a particularly important role in learning about patterns. Implications are discussed in terms of the benefits of relational knowledge and EF for preschoolers’ development of patterning and mathematics skills.

Eliciting explanations: Constraints on when self-explanation aids learning

Generating explanations for oneself in an attempt to make sense of new information (i.e., self-explanation) is often a powerful learning technique. Despite its general effectiveness, in a growing number of studies, prompting for self-explanation improved some aspects of learning, but reduced learning of other aspects. Drawing on this recent research, as well as on research comparing self-explanation under different conditions, we propose four constraints on the effectiveness of self-explanation. First, self-explanation promotes attention to particular types of information, so it is better suited to promote particular learning outcomes in particular types of domains, such as transfer in domains guided by general principles or heuristics. Second, self-explaining a variety of types of information can improve learning, but explaining one’s own solution methods or choices may reduce learning under certain conditions. Third, explanation prompts focus effort on particular aspects of the to-be-learned material, potentially drawing effort away from other important information. Explanation prompts must be carefully designed to align with target learning outcomes. Fourth, prompted self-explanation often promotes learning better than unguided studying, but alternative instructional techniques may be more effective under some conditions. Attention to these constraints should optimize the effectiveness of self-explanation as an instructional technique in future research and practice.

Wait for It . . . Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study.

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical equivalence problems either before or after receiving brief conceptual instruction. In Experiment 1 (n = 41), the explore-instruct approach was less effective at supporting learning than an instruct-solve approach. However, it did not include a common, but often overlooked feature of an explore-instruct approach, which is provision of a knowledge-application activity after instruction. In Experiment 2 (n = 47), we included a knowledge-application activity by having all children check their answers on previously solved problems. The explore-instruct approach in this experiment led to superior learning than an instruct-solve approach. Findings suggest promise for an explore-instruct approach, provided learners have the opportunity to apply knowledge from instruction. Correspondence: Abbey Marie Loehr, 230 Appleton Place, Peabody #552, Vanderbilt University, Nashville, TN 37203; Phone: (615) 343-7149. Email: abbey.loehr@vanderbilt.edu

Putting the “th” in Tenths: Providing Place-Value Labels Helps Reveal the Structure of Our Base-10 Numeral System

ABSTRACT Research has demonstrated that providing labels helps children notice key features of examples. Much less is known about how different labels impact children’s ability to make inferences about the structure underlying mathematical notation. We tested the impact of labeling decimals such as 0.34 using formal place-value labels (“3 tenths and 4 hundredths”) compared to informal labels (“point three four”) or no labels on children’s problem-solving performance. Third- and fourth-graders (N = 104) learned to label decimals while playing a magnitude comparison game and placing decimals on a number line. Formal labels facilitated performance on problems that required understanding the role of zero. Further, formal labels led to lower performance on problems where a whole-number bias led to a correct answer, suggesting that formal labels may have reduced a whole-number bias. Overall, formal labels helped highlight the place-value structure of decimals, indicating that labels can help children notice mathematical structure.

Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson

BACKGROUND Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. AIMS This study evaluated the effect of instruction on a math concept and procedure within the same lesson relative to a comparable amount of instruction on the concept alone. Direct instruction was provided before or after solving problems to evaluate whether the type of instruction interacted with the timing of instruction within a lesson. SAMPLE We worked with 180 second-grade children in the United States. METHODS In a randomized experiment, children received a classroom lesson on mathematical equivalence in one of four conditions that varied in instruction type (conceptual or combined conceptual and procedural) and in instruction order (instruction before or after solving problems). RESULTS Children who received two iterations of conceptual instruction had better retention of conceptual and procedural knowledge than children who received both conceptual and procedural instruction in the same lesson. Order of instruction did not impact outcomes. CONCLUSIONS Findings suggest that within a single lesson, spending more time on conceptual instruction may be more beneficial than time spent teaching a procedure when the goal is to promote more robust understanding of target concepts and procedures.