Collaborative Research: Using Cognitive Science Principles to Help Children Learn Place Value

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The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.Many children have trouble understanding what multidigit numbers mean and this can lead to long-term problems in mathematics. Poor place value understanding plagues children from all socioeconomic backgrounds and is not limited to those with learning disabilities. This problem is widespread and pervasive; indeed, perhaps more widespread than currently understood because some tests may overestimate what children know. The critical skill needed for long-term success, and one not always measured, is called decomposition. It involves knowing how to break a multi-digit number down into its components by place (ones, tens, hundreds) and interpret its meaning (e.g., 642 = 6 hundreds, 4 tens, and 2 ones). This project will target that crucial skill and test new ways of teaching place value based on principles of analogical reasoning, gleaned from decades of cognitive science research. These new approaches will make place value more transparent by highlighting and aligning its structure across spoken number names, written numerals, and sets of objects. By leveraging these powerful analogical learning mechanisms, it may be possible to teach place value earlier than is typical, so the project will target K-1 students. If successful, this approach could head off the misconceptions that are currently common among older children. The project will also track children over time, using tests that measure decomposition and other place value concepts to see how they interrelate. The project's activities have been designed to be inexpensive and fit into everyday educational practice, so that the results may be easily implemented by teachers.The project will test new instructional approaches designed to help K-1 students comprehend place value. The project is innovative in that it will emphasize the underlying relational structure of place value symbols, and target this structure with instructional materials and techniques drawn from the structure mapping literature. Its theory of action is that instruction which scaffolds structure mapping for place value will better prepare children to face the challenges of advanced operations, such as multi-digit calculation. The project specifically targets decomposition, as this has been identified as a particular stumbling block for children. Also, decomposition skill has been linked to better long-term mathematics outcomes. There will be three studies. Study 1 will track the development of place value understanding from kindergarten to 2nd grade, using some measures that clearly require decomposition, and others that are in wide use but may not require decomposition, such as number line estimation and magnitude judgments. The study will show how these measures are related over developmental time, as well as testing whether a firm understanding of decomposition predicts later mathematics learning. Studies 2 and 3 will use a pretest-training-posttest design to test the efficacy of six structure mapping activities for place value in K-1 students. The training in Study 2 will be focused on one activity for three weeks, whereas the training in Study 3 will include all six activities presented over an entire semester.