## Friday, December 2, 2011

### Measurement in K-2

K.MD Describe and compare measurable attributes
1.MD Measure lengths indirectly and by iterating length units
2.MD Measure and estimate lengths in standard units

I wrote about teaching of measurement in primary grades almost 3 years ago (Dec. 2008), In the post, I stated that there are 3 related yet distinct goals while teaching measurement:
* understanding the attribute being measured
* process of measurement
* how to use measuring instruments.

Also, there is a general consensus that teaching of measurement should proceed along the following instructional sequence:
1. Direct comparison
2. Indirect comparison
3. Measuring with non-standard units
4. Measuring with standard units

From this perspective, I wrote that the GPS was unclear about steps 2 and 3. In contrast, the Common Core follows the suggested sequence explicitly, at least with the attribute of length. For other attributes like (liquid) volume, mass, area, angle, etc., the CCSS appears to jump right in with step 4, measuring with standard units. For example, 3.MD.2 states, "Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l)." Although I certainly do not advocate going through the 4 steps of measurement instruction with every attribute, I am not sure if experiences with one attribute (length) is enough for children to generalize the process of measurement. In the typical Japanese curriculum, children study length and capacity (liquid volume) in Grades 1 and 2 (the first 2 years of elementary schools in Japan), and they go through these 4 steps with each attribute. They will also include some direct comparison activities with comparison of areas before they study how to calculate area. As we move ahead with the implementation of the CCSS, we may want to include some comparison activities as well as measuring with non-standard units for some of the attributes. Furthermore, explicit discussions on the process of measurement (selecting a unit, using a unit to iterate/cover the object, count the number of units) so that with the later attributes, we can start with the question of what we should use as a (standard) unit.