The content knowledge a teacher must have in order to enact high quality mathematics instruction includes, but is not limited to, place value, quality relationships with students, an understanding of the learning trajectories, and knowing one’s own beliefs and mathematical identity.
Knowledge of place value and an understanding of the base-ten system is critical content a teacher must have in order to enact high quality mathematics instruction. In the lower grades where I have taught for seven years, I recognize the importance of a strong base in place value in order to make connections later in addition and subtraction.
Roger Howe (2011) writes an article titled “Three Pillars of First Grade Mathematics” about a problem of practice in teaching mathematics to elementary-age children. “The standard conception of place value in the US is rather limited: we treat it as a vocabulary issue, that students …show more content…
Children progress in a natural way, i.e. they must crawl before they walk. This is true in mathematics also. There are foundational concrete skills students must obtain before being able to mentally manipulate numbers. “When teachers understand these developmental progressions, and sequence activities based on them, they build mathematics learning environments that are particularly developmentally appropriate and effective” (Clements and Sarama, 2009, p. 2)
If teachers do not understand the importance of the path of learning and levels of thinking, they could impede student learning by going beyond their developmental capacity. Understanding learning trajectories increases the likelihood of high quality mathematics instruction by narrowing the goals of learning, describing the thinking and learning processes of children at various levels, and highlighting learning activities in which students might engage (Clements & Sarama, 2009, p.
Knowledge of place value and an understanding of the base-ten system is critical content a teacher must have in order to enact high quality mathematics instruction. In the lower grades where I have taught for seven years, I recognize the importance of a strong base in place value in order to make connections later in addition and subtraction.
Roger Howe (2011) writes an article titled “Three Pillars of First Grade Mathematics” about a problem of practice in teaching mathematics to elementary-age children. “The standard conception of place value in the US is rather limited: we treat it as a vocabulary issue, that students …show more content…
Children progress in a natural way, i.e. they must crawl before they walk. This is true in mathematics also. There are foundational concrete skills students must obtain before being able to mentally manipulate numbers. “When teachers understand these developmental progressions, and sequence activities based on them, they build mathematics learning environments that are particularly developmentally appropriate and effective” (Clements and Sarama, 2009, p. 2)
If teachers do not understand the importance of the path of learning and levels of thinking, they could impede student learning by going beyond their developmental capacity. Understanding learning trajectories increases the likelihood of high quality mathematics instruction by narrowing the goals of learning, describing the thinking and learning processes of children at various levels, and highlighting learning activities in which students might engage (Clements & Sarama, 2009, p.