Length measurement in the early years: teaching and learning with learning trajectories

Comparison of Pre-service Elementary Teachers’ Mathematical Knowledge in Teaching for Length Measurement: Turkey and the United States

“…Since the pre-service teachers' statements were similar to this emphasis, it can be concluded that these teachers also have difficulties in length measurement. Another student difficulty arises when the length of a ruler is not enough to cover the length of an object to be measured (Bragg & Outhred, 2004;Sarama et al, 2021). A similar finding was disappointingly found in this study as one US pre-service teacher mentioned that the ruler is not long enough to measure the fabric.…”

“…Therefore, they cannot measure if the number of the unit is not sufficient to fully cover the length of an object (Bragg & Outhred, 2004). If the chosen unit does not fully cover the length of an object or if it gets longer when one more of the chosen unit is added, students, then, think that they have to change the unit that they chose (Sarama et al, 2021). Furthermore, since they do not know how the iteration process is related to the number as a measurement, they can use different-sized units together to measure a length (Clements & Sarama 2009;Lehrer et al, 2003).…”

“…Furthermore, since they do not know how the iteration process is related to the number as a measurement, they can use different-sized units together to measure a length (Clements & Sarama 2009;Lehrer et al, 2003). The important thing for students is that the length must be filled out with units whose sizes may be different or equal (Sarama et al, 2021). That is, the students have difficulties in discovering the inverse relationship between the unit size and the number of units to measure a length.…”

“…Not only that, but, when these students were asked to state the length of an object, they just state the numerals without including the units (e.g. five instead of five cm) (Sarama et al, 2021). Smith et al (2013) attributes the reason for this difficulty to not understanding the structure of the ruler.…”

Testing a Theoretical Assumption of a Learning-Trajectories Approach in Teaching Length Measurement to Kindergartners

“…Instructional Conditions. To test the significance of the instructional sequence-of-levels assumption in the context of an experimental study, the primary experimental group (LT) received one-on-one instruction that followed an empirically validated learning trajectory for length (Barrett et al, 2011(Barrett et al, , 2017Sarama et al, 2011Sarama et al, , 2021Szilagyi et al, 2013). We compared growth in their length-measurement knowledge to two counterfactual groups.…”