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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_pic– 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.


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.

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4 Responses

  1. Are the neu­ro­phys­i­cal cor­re­lates of work­ing mem­ory deficits the result of bio­log­i­cal­ly ordained structural/processing insuf­fi­cien­cies (mal­adap­tive bio-devel­op­ment) (1) or are the neu­ro-phys­i­o­log­i­cal cor­re­lates of work­ing mem­o­ry deficits the result of a lack of neu­ro­phys­i­cal exercise/activity due to learned mal­ad­pa­tive pro­cess­ing schema? For a relat­ed exam­ple, a recent study of dyslex­ia moved us clos­er to under­stand­ing the sig­na­ture of dyslex­ia pri­or to begin­ning read­ing ( but here too the test­ing is far down­stream from the influ­ence of ear­ly learn­ing. Isn’t dis­en­tan­gling the genet­i­cal­ly-deter­mined from the learn­ing-formed much more sub­tle than we are acknowl­edg­ing? Are the brain dif­fer­ences cor­re­lat­ed with mem­o­ry deficits described here exclu­sive­ly the result of gene-for­ma­tive process­es or could there be a much deep­er and rich­er and more sub­tle realm of ear­ly learn­ing that can also result in the brain dif­fer­ences you are describ­ing?

  2. Tracy says:

    Hi David, thanks for tak­ing the time to com­ment. It looks like there are at least 3 ques­tions here, so I will try to address them in turn (and briefly!). The first ques­tion seems to me to be why some chil­dren have WM deficits, while oth­ers don’t. This is a tricky one and the jury is still out. We do know that WM is not great­ly affect­ed by envi­ron­men­tal fac­tors (eg, finan­cial back­ground, moth­er’s edu­ca­tion­al lev­el, etc), unlike oth­er cog­ni­tive skills in gen­er­al abil­i­ty (IQ scores). So why do some kids strug­gle: one pos­si­bil­i­ty is they start off with a small­er WM (or ‘post-it-note’ as I have referred to it in the past). Anoth­er pos­si­bil­i­ty is that for some rea­son they are not able to use all of their WM capac­i­ty, some­times b/c of stress or anx­i­ety. So although they have the capac­i­ty to do well, they are not max­i­miz­ing it.
    Q2: Genet­ics. There is some research (and I am in the midst of com­plet­ing some as well) indi­cat­ing there is a a strong genet­ic com­po­nent to WM capac­i­ty. This idea fits well with my pre­vi­ous point about WM being min­i­mal­ly affect­ed by envi­ron­men­tal fac­tors.
    Q3: Brain dif­fer­ences: The ques­tion could be rephrased to look at whether there is less acti­va­tion when some peo­ple use WM to solve a prob­lem, vs brain size (cor­ti­cal thick­ness, etc). We do know that low­er scores on WM tests are linked to less brain acti­va­tion in the PFC. How­ev­er, there is less research on actu­al brain size and WM scores. Hope this helps.

  3. Thank for this arti­cle Doc­tor. Would the math issue be less­ened if the musi­cal part of the brain was used to assist?

    My father vol­un­teered using pro­to­cols from what was the Philadel­phia Brain Injury Clin­ic. Despite hav­ing lost 1/2 his brain in a trag­ic auto acci­dent (he was a bystander) with a very reg­i­ment­ed 14 hour+ day of ther­a­py his recov­ery from giv­en up for dead to mid lev­el func­tion was amaz­ing.

    Thank you for shar­ing this insight.

    I’m a gen­er­al­ist in the field of resilien­cy.
    One of our pro­grams helps fos­ter par­ents, grand par­ents, par­ents of spe­cial needs chil­dren learn key skills to assist them gain some added self-aware­ness and self-man­age­ment skills

    Toron­to Cana­da

  4. P.S. I should have said my father was one of the vol­un­teers help­ing the gen­tle­man that had been seri­ous­ly injured.

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