Horizon mathematics knowledge, i.e., teachers’ understanding of how various mathematical topics are interrelated, can help mathematics teachers organize the discrete parts of mathematical content to develop coherent teaching lessons. For example, when teaching whole number addition and subtraction, connections to concepts such as base-10 concepts and the inverse relationship between addition and subtraction could help students solve the addition and subtraction problem better. Thus, teacher training programs have been increasingly promoting this knowledge among pre-service teachers (PSTs) to help them enhance their teaching skills and better prepare them for future teaching. However, little is known about what kind of horizontal knowledge PSTs have developed and how well they utilize it in their teachings. By analyzing video presentations of 43 elementary PSTs, this study examined their horizon mathematics knowledge related to backward and forward conceptual connections of whole number addition and subtraction concepts. The findings revealed that PSTs tend to make connections with previously learned mathematics concepts (i.e., backward conceptual connections) but pay relatively less attention to connecting with other relevant mathematics concepts students will learn in future grades (i.e., forward conceptual connections). In addition, the findings showed that PSTs displayed various types of inaccuracies when connecting base-10 place value and regrouping. These findings offer important insights for teacher training programs to adapt their mathematic method courses to help PSTs improve their horizontal knowledge and proactively address inaccuracies observed in the present study.
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