Students in 2nd and 3rd grade who have whole number misconceptions — such as claiming 23 is the largest two-digit number when the correct answer is 99 — are more likely to make uncommon computational errors as late as the 8th grade.
This is the result of a longitudinal study, published recently in the journal Frontiers in Psychology, led by Michele Mazzocco, Institute of Child Development professor and research director for the Center for Early Education and Development.
In the study, 224 2nd and 3rd graders’ were asked to report the smallest and largest single digit, two-digit and three-digit numbers. After each answer, the students were asked if they were sure of their answer.
Two hundred of the 224 answered correctly that 9 is the largest single digit number while 180 knew that 99 was the largest two-digit number. Only 87 were able to identify 999 as the largest three-digit number. It’s important to note that these results reflect typical developments in learning about multi-digit numbers among these age groups.
“The fact that many 2nd graders didn’t know the largest three digit number is not particularly informative, said Mazzocco. “However, of the students who gave an incorrect response, what we looked at was the number they gave. For instance, if a student responded that 900 is the largest three-digit number — although it’s incorrect, the answer is logical. More importantly, 900 is a common error made by 2nd and 3rd graders answering this question. When a student gave an illogical, infrequent response, such as 236 or 653, that student may not only have incomplete place value concepts but may also lack a solid understanding of one-digit whole numbers, such as 6, 5 and 3.”
For students who made these uncommon errors in 2nd and 3rd grades, the study found that the lack of number knowledge predicted specific types of place value errors made, by the same children, on math assessments at grade 8. It also showed that young students who have early whole number misconceptions go on to have slower and less accurate performance and persistent, atypical computational errors in later school years.
“This research suggests that specific qualitative assessments of symbolic number knowledge in early grades may reveal more about children’s thinking about numbers than does a typical ‘pass or fail’ test. This in turn may reveal which students are most at risk for persistent poor math outcomes in future years,” said Mazzocco.
Classifying students with mathematics learning disability (MLD, or dyscalculia) is typically based on composite scores from broad measures of math achievement, according to Mazzocco. These scores may predict later math achievement levels but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term failure in math.
“One of our goals with the study was to help define what poor number concepts might look like in early childhood and to help teachers identify which students have not developed a good number sense early on,” said Mazzocco.
Early response to the study from educators and researchers has generated interest in more qualitative research on identifying MLD in young children, Mazzocco said.
“Number misconceptions are fairly typical in very young children, and they are not always cause for alarm. Our current work is designed to focus on which number concept errors in preschool predict persistent number misconceptions throughout school, and our next steps are to study how early misconceptions alter the path of early mathematics learning,” added Mazzocco.
See more in this Minnesota Public Radio story.