In the overview module, we discuss the important and bi-directional relationships between executive functioning (EF) and early math learning (see Overview of Executive Functioning and Math). Here we discuss the role of executive functioning in measurement. As mentioned in The Mathematics of Measurement, children’s early experiences with measurement frequently involve making comparisons (e.g. big vs. small, tall vs. short, heavy vs. light, longer vs. shorter) and ordering three or more objects according to a specific dimension of the object. Importantly, both comparisons and ordering in measurement involve some degree of executive functioning, particularly in terms of cognitive flexibility. 

• Comparisons: From a young age, children enjoy making comparisons (e.g. “my tower is taller than yours”; “my cup has less juice than yours”). Importantly, the ability to compare objects involves attending to the relevant dimensions of an object. For example, when comparing two block towers, a child may choose to attend to height and say one tower is taller than the other. However, if the same child chooses to attend to width, they may say that the two towers are the same. Understanding that the same objects can be compared according to different dimensions and that the outcome of the comparison may differ depending on the dimension of focus involves cognitive flexibility.
   
• Ordering three or more objects: Another key aspect of measurement in preschool is the ability to order three or more objects according to specific dimensions of the object. When ordering objects such as block towers, children come to understand that the middle tower is both taller than the shortest tower and shorter than the tallest tower. The ability to understand that the same object can be described differently (i.e. taller or shorter) depending on the comparison of focus involves cognitive flexibility. Further, as children gain more experience with ordering objects, they come to understand that the same group of objects can take on a different order depending on the dimension used. For example, the order of the towers may differ if the child is ordering by width rather than height.

The examples above demonstrate that two of the key aspects of measurement in preschool call upon young children’s executive functioning skills (particularly cognitive flexibility). Because of this relationship between EF and measurement, teachers should think of measurement as an opportunity to support both a key mathematical concept and executive functioning.

Below we offer some tips for how early childhood educators can incorporate more explicit EF support into activities involving measurement.

Working Memory: Students practice working memory skills when they are required to hold and/or manipulate multiple pieces of information in mind over short periods of time in order to problem-solve.

• Teachers can support working memory by engaging their students in measurement activities that involve arithmetic. For example, the teacher may say “I have a tower that is 5 blocks tall. How tall would my tower be if I added 3 blocks?” Here the child has to hold multiple pieces of information in mind (i.e. how many blocks tall the tower currently is and how many they have to add) in order to arrive at the correct answer.
• Comparisons of abstract dimensions also involve working memory. Ask children to consider whether it is hotter in the winter or summer or whether it takes longer to take toys and materials out to play with or to put them away (this can encourage interesting conversations about clean up time as well!).

Inhibitory Control: Students practice inhibitory control skills when they engage in activities that require them to wait their turn and/or think before they act. Providing practice before engaging in these group activities can help build these skills.

• Teachers can support inhibitory control by playing measurement games in which students are only supposed to respond when they receive a certain cue. For example, the teacher may say “Point to something that is bigger than you, only if you are wearing a red shirt!” followed by “Point to something that is smaller than you, only if you are wearing a blue shirt!” Here children are making comparisons based on size while also practicing reflecting and waiting before they act.

Cognitive Flexibility: Teachers can support cognitive flexibility by encouraging students to make comparisons, shift perspectives and to approach activities in different ways.

• Teachers can support cognitive flexibility during measurement activities by encouraging students to make comparisons according to length, weight, size etc. For example, the teacher might say “Look at the tower I just built, can you build one taller than mine? Now can you build one wider than mine?”
• Similarly, teachers can support cognitive flexibility by encouraging students to order objects according to different dimensions of the object. For example, the teacher might say “Can you put these trees in order from shortest to tallest? Followed by, “Now can you put them in order from the most narrow to widest?” In this way, the child comes to realize that the same objects can be ordered differently according to different dimensions of the object. Additionally, if the child is asked to do multiple rounds of ordering from shortest to tallest and then to switch to order from most narrow to widest, this would also support inhibitory control as the child would have to inhibit their original response (ordering from shortest to tallest) in favor of the new rule (ordering from the most narrow to widest)

Planning and Organization: Students practice their planning and organization skills when they engage in multi-part activities that require the organization of materials and/or adherence to a sequence of steps.

• Teachers can support planning and organizational skills during measurement activities by encouraging students to set a goal and to think through what materials they need to meet that goal. For example, the teacher might say “Do you want to build a tall tower or a short tower?” (goal setting), followed by “How many blocks do you need to build that tower?” (organizing materials).
• Related questions about how long it might take to build a very tall tower relative to a small tower can engender rich conversations about more or less construction time when using larger or smaller blocks.