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Bilingualism predicts mathematical competence

7 Feb

An interesting paper, just published in Learning and Individual Differences. Here are the highlights:

• Using large-scale datasets, we examined the relation between bilingualism and math achievement.

• We found that bilingualism significantly predicted preschoolers’ math achievement.

• The positive predictability of bilingualism persisted from kindergarten through first grade.

• Bilingual advantages in executive functioning likely extend to mathematical achievement.

Mindfulness meditation reduces symptoms of depression

10 Nov

Here is a well designed study looking at the effects of mindfulness meditation on depression. The abstract reads:


Training in mindfulness has been introduced to the treatment of depression as a means of relapse prevention. However, given its buffering effects on maladaptive responses to negative mood, mindfulness training would be expected to be particularly helpful in those who are currently suffering from symptoms. This study investigated whether a brief and targeted mindfulness-based intervention can reduce symptoms in acutely depressed patients.


Seventy-four patients with a chronic or recurrent lifetime history were randomly allocated to receive either a brief mindfulness-based intervention (MBI) encompassing three individual sessions and regular home practice or a control condition that combined psycho-educational components and regular rest periods using the same format as the MBI. Self-reported severity of symptoms, mindfulness in every day life, ruminative tendencies and cognitive reactivity were assessed before and after intervention.


Treatment completers in the MBI condition showed pronounced and significantly stronger reductions in symptoms than those in the control condition. In the MBI group only, patients showed significant increases in mindfulness, and significant reductions in ruminative tendencies and cognitive reactivity.


Brief targeted mindfulness interventions can help to reduce symptoms and buffer maladaptive responses to negative mood in acutely depressed patients with chronic or recurrent lifetime history.

Manipulatives may hinder learning

10 Apr

Walk into an early elementary school classroom and you are likely to see lots of manipulatives. From Popsicle sticks to Cuisenaire rods we have a strong intuitive sense that these objects should help children learn mathematics.

Not so fast, says Sara Fulmer over at The Learning Scientist;

Although manipulatives can increase students’ attention, this attention may not benefit their learning. In fact, the very aspect of manipulatives that capture students’ attention—bright colors, visual appeal, realistic features—may be their downfall. Manipulatives that are more visually interesting or realistic can increase off-task behavior, such as building or sorting (1). This is especially true if students interact with that object in other contexts, such as during play time or outside of the classroom.

Students who learn with manipulatives can become too reliant on the object and context, and as a result, have difficulty transferring their knowledge to new contexts, different testing formats, or to abstract representations (e.g., algebraic expressions) of the problem

Raymond Smullyan

13 Feb

I am surrounded by the books of Raymond Smullyan and I was very sad to read of his death at age 97 in today’s New York Times. When time allows, I have been been very slowly working my way through his Set Theory and the Continuum Problem (co-authored with Melvin Fitting). For a more gentle introduction to his thought try Who Knows?: A Study of Religious Consciousness or his autobiography Some Interesting Memories: A Paradoxical Life.

Here is piece composed by Jeanell Carrigan in honor of Smullyan:

Inside the mind of a math savant

21 Oct

From the good people at Numberphile;

Handedness and mathematical skills

11 May

According to a press release from the University of Liverpool:

“Psychologists from the University of Liverpool and the University of Milan conducted a study involving more than 2,000 students in Italy aged between six to 17 years and asked them to complete a number of mathematical tasks, including simple arithmetic and problem-solving.

In the study, the participants’ degree of handedness was ascertained by the Edinburgh Handedness Inventory, a questionnaire assessing how much an individual is right- or left-handed (or ambidextrous). The researchers then analysed the results in relation to the extent to which they were right or left-handed.

Liverpool psychologist, Giovanni Sala, who conducted the study, said: “This study found there is a moderate, yet significant, correlation between handedness and mathematical skill. Moreover, the amount of variance in the maths scores explained by handedness was about 5-10%, a surprisingly high percentage for a variable like handedness.”

This was a conference paper, I will reserve judgment until I read the actual research.


Note: This video claims that Gandhi was left handed. When I looked on line for images of him writing, the ones I could find show him writing with his right hand. Of course, it’s always possible that the images were flipped. Does anyone know a credible source about Gandhi’s handedness?

The brains of mathematicians

9 May

A post at Scientific American asks: “How Does a Mathematician’s Brain Differ from That of a Mere Mortal?”

“The team used functional magnetic resonance imaging (fMRI) to scan the brains of 15 professional mathematicians and 15 nonmathematicians of the same academic standing. While in the scanner the subjects listened to a series of 72 high-level mathematical statements, divided evenly among algebra, analysis, geometry and topology, as well as 18 high-level nonmathematical (mostly historical) statements. They had four seconds to reflect on each proposition and determine whether it was true, false or meaningless.
The researchers found that in the mathematicians only, listening to math-related statements activated a network involving bilateral intraparietal, dorsal prefrontal, and inferior temporal regions of the brain.”


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