When 1 + 1 = 5: Dyscalculia and Working Memory

Jacob’s moth­er writes that ‘Jacob, 10-years-old, still strug­gles with num­ber bonds to 10. Learn­ing to tell the time is still slow – he has not mas­tered half-past. Although he man­aged to learn his 5x tables because we prac­ticed all sum­mer, this has now gone’.

Jacob has dyscal­cu­lia, a math dis­abil­i­ty where stu­dents strug­gle to learn or under­stand math­e­mat­ics. Stu­dents with dyscal­cu­lia find it dif­fi­cult to deci­pher math sym­bols (e.g. +, –), count­ing prin­ci­ples (‘two’ stands for 2), solv­ing arith­metic prob­lems, and usu­al­ly trans­pose num­bers (e.g. 75 becomes 57). How­ev­er, dyscal­cu­lia encom­pass­es more than prob­lems with num­bers – there is also a strug­gle with telling the time as in Jacob’s case, iden­ti­fy­ing left from right, and rec­og­niz­ing patterns.

But why do some stu­dents strug­gle to learn num­bers and cer­tain math­e­mat­i­cal principles?

Work­ing Mem­o­ry plays a key role. To solve a math­e­mat­i­cal prob­lem like 1 + 1, we need to use our Visuo-Spa­tial Work­ing Mem­o­ry. Visuo–spatial work­ing mem­o­ry func­tions like a big men­tal black­board that gives us a space to write all of the num­bers nec­es­sary to solve a problem.

It also works togeth­er with the brain’s cal­cu­la­tor known as the Intra­pari­etal Sul­cus (IPS), locat­ed in the right hemi­sphere. Brain imag­ing stud­ies that looked at brain activ­i­ty while peo­ple were count­ing and cal­cu­lat­ing quan­ti­ties reveal that when we count, regard­less of whether it is shapes, num­bers, or objects, the IPS is acti­vat­ed. In dyscal­culics, this area under­per­forms and may under­pin their maths difficulties.

Like Jacob, the stu­dent with dyscal­cu­lia has clear work­ing mem­o­ry deficits. How­ev­er, the link between work­ing mem­o­ry and math skills depends on the age of the child as well as the type of math task. Ver­bal work­ing mem­o­ry plays a strong role in math skills in sev­en-year-olds and is a reli­able indi­ca­tor of dyscal­cu­lia in the first year of for­mal school­ing. Once chil­dren reach ado­les­cence, ver­bal work­ing mem­o­ry is no longer sig­nif­i­cant­ly linked to math­e­mat­i­cal skills. One expla­na­tion for this change is that ver­bal work­ing mem­o­ry plays a cru­cial role for basic arith­metic skills like learn­ing arith­metic rules and retain­ing rel­e­vant data such as car­ried dig­its when they are young. How­ev­er, as chil­dren get old­er oth­er fac­tors such as num­ber knowl­edge and strate­gies play a greater role.

If you are work­ing with a stu­dent with dyscal­cu­lia, it is impor­tant not only to address their dif­fi­cul­ties with num­bers, but to also assess their Work­ing Mem­o­ry. It is pos­si­ble that they have a small men­tal black­board (visuo-spa­tial Work­ing Mem­o­ry) that is mak­ing it hard­er for them to apply their num­ber knowl­edge in a class­room situation.

– Tra­cy Pack­iam Alloway, PhD, is an Assis­tant Pro­fes­sor at the Uni­ver­si­ty of North Flori­da. She was recent­ly award­ed the pres­ti­gious Joseph Lis­ter Award by the British Sci­ence Asso­ci­a­tion for her con­tri­bu­tion to sci­ence. Tra­cy devel­oped a stan­dard­ized work­ing-mem­o­ry tests for edu­ca­tors pub­lished by Psy­cho­log­i­cal Cor­po­ra­tion, which to date has been trans­lated into 15 lan­guages and used to screen for work­ing mem­ory prob­lems in stu­dents with dyslex­ia, motor dys­praxia (Devel­op­men­tal Coor­di­na­tion Dis­or­der), ADHD and Autis­tic Spec­trum Dis­or­der. She pro­vides con­sul­tancy to the World Bank and her research has received wide­spread inter­na­tional cov­er­age in hun­dreds of media out­lets, includ­ing Sci­en­tific Amer­i­can, the BBC, Reuters, ABC News, and NBC.

Ref­er­ence

Alloway, T.P. & Pas­sol­unghi, MC. (2011). The rela­tions between work­ing mem­o­ry and arith­meti­cal abil­i­ties: A com­par­i­son between Ital­ian and British chil­dren. Learn­ing and Indi­vid­ual Dif­fer­ences, 21, 133–137.

To learn more:

• 10% Stu­dents may have work­ing mem­ory prob­lems: Why does it mat­ter, by Tra­cy Alloway
• Try Think­ing and Learn­ing with­out work­ing mem­ory, by Bill Klemm