Prof. Daniel Ansari: Building Blocks of
Mathematical
Competence
Prof. Daniel Ansari is
one of the leading researchers in the study of the development of mathematical skills.
Here he talks with an
audience of educators. Ansari speaks
clearly and is a joy to listen to. This talk
is recommended despite the annoying fact that the photographer concentrated
only on him and did not photo the slides he shows.
Here are several
messages from the lecture:
Early
math skills (in preschool and the early grades of elementary school) predict
not only later math skills but also later reading skills. Ansari
deduces that working on early math skills helps not only later math but also
later reading. I think it might be
possible that the same cognitive abilities lie both at the base of early math
skills and at the base of later math skills and later reading skills (for
example, working memory or fluid ability or even comprehension knowledge). So I would think that it's a good idea to improve
these skills as well as early math skills.
Ansari reviews (briefly) research that shows
the ability of babies and animals to discriminate between quantities.
Ansari highlights the importance
of young children's ability to process mathematical symbols (the digits 1,2,3…are mathematical symbols. Each of them represents a specific
quantity). Children with
difficulties in math find it hard to match math symbols with quantities (for example, to match the symbol "3"
and three objects). The ability to name
digits and to match digits with quantities are very important for the
progression from kindergarten to first grade – from formal to informal math
education. We need to make sure
that kindergarten (five to six year old) children are able to name math symbols
(to name digits) and to link digits with quantities. It's
important to practice counting, digit comparisons and quantity comparisons,
ordering digits, matching digits and quantities and so on with kindergarten
children,
The number line helps children to understand
relations between numbers. There is a
very strong connection between number concepts and visuospatial concepts. Playing games like "ladders and snakes"
helps children understand this relation and relations between numbers.
Ansari thinks that the difficulties of
children with dyscalculia do not originate from the non-symbolic system (quantity
perception) but from difficulties in linking symbolic and non-symbolic systems
(linking quantity to digit). This is an
optimistic viewpoint because it's possible to work on these links, while it's
difficult to improve quantity perception itself.
Ansari talks about developmental dyscalculia
and different cognitive abilities that are tied with difficulties in math
(working memory in general and especially visupspatial working memory,
phonological awareness, executive functions and language).
As for math anxiety, Ansari says that children
"inherit" their parent's math anxiety. When a child is doing homework with his math
anxious parent (even if they are working on basic math), tension rises and
makes the child's math anxiety even worse.
A parent with math anxiety does not talk with his children about math
concepts - even about simple, basic quantities or matching quantities to
numbers. This affects the development of
his children's math skills.
Furthermore, teachers with math anxiety cause
their students to "catch" math anxiety too. Math anxiety of teachers, assessed at the beginning
of first grade, predicted math anxiety of these teacher's students at the end
of first grade.
At the end of the lecture, Ansari talks about
several myths in education that are not related to math, like the erroneous
myth about learning styles.
A very interesting lecture!
