A direct comparison of two measures of ordinal knowledge among 8-year-olds

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Title

Authors

Chang Xu, Jo-Anne LeFevre, Sabrina Di Lonardo Burr, Erin A. Maloney, Judith Wylie, Victoria Simms, Sheri-Lynn Skwarchuk, Helena P. Osana (2023)

Journal and DOI

Previous Research

Ordinal knowledge – that is, the ability to count objects in order and understand when numbers are greater than, less than, or equal to others – is related to mathematical learning in children
Ordinal knowledge has been measured using judgment (i.e., deciding whether a sequence of three digits is in order) and ordering tasks (i.e., order three digits from smallest to largest).
Children’s ordinal skills (I.e., understanding order of numbers) seem to develop more slowly than their cardinal skills (I.e. understanding quantity of numbers).
Arithmetic skills can be best predicted by ordering tasks OR order judgement tasks depending on the age group of the child.
- There is substantial evidence that ordinal skills replace the role of number comparison as the key predictor of arithmetic from Grade 2 onward.

What did we ask?

Do ordering and order judgment tasks share the same underlying cognitive processes for children in Grade 3?
Note: Grade 3 was chosen because the dominant role of ordinal skills in predicting arithmetic skills becomes stable by Grade 3

How did we do it?

Participants were 87 Grade 3 children in Ontario with an average age of 8.7 years
Children were tested individually during three testing sessions within three months.
Children completed tasks for the following:

First session:

Number Comparison: On an iPad, children were presented with side-by-side single-digit numbers (i.e., digits 1 to 9) and were instructed to tap the numerically bigger number as quickly as possible.
Ordering Task: On an iPad, children were asked to tap numbers in order from smallest to largest as quickly and accurately as possible.

Second session:

Working Memory: The digit backward span task assessed children’s working memory capacity. Participants listened to a sequence of numbers and were asked to repeat them in reverse order.
Order Judgment Task: On an iPad, children were asked to decide whether sequences were in ascending order or not, as fast as possible.

Third session:

Arithmetic Fluency: Children were asked to complete addition and subtraction questions using paper-and-pencil as quickly and accurately as possible.

What did we find?

Ordering and order judgment tasks involve similar cognitive processes for children in Grade 3.
Working memory and number comparison skills predicted ordinal skills for both tasks.
Performance on ordinal tasks was related to children’s familiarity with number sequences, knowledge of relative magnitude, and working memory skill.
Consistent with the literature, ordinal knowledge superseded the role of number comparison as the key predictor of arithmetic.
Both the ordering and order judgment tasks involved cardinal and ordinal processing of symbolic numerals.

Take away Message

Ordering and order judgment tasks involve similar thinking processes.
Both methods (I.e., order and order judgement tasks) of testing this skill are effective, but combining them into one measure might be even more effective.

Brought to you by Dr. Erin Maloney’s Cognition and Emotion Lab at the University of Ottawa.