Discrete Analysis — an arXiv overlay journal

Tim Gowers starts a new journal:

This post is to announce the start of a new mathematics journal, to be called Discrete Analysis. While in most respects it will be just like any other journal, it will be unusual in one important way: it will be purely an arXiv overlay journal. That is, rather than publishing, or even electronically hosting, papers, it will consist of a list of links to arXiv preprints. Other than that, the journal will be entirely conventional: authors will submit links to arXiv preprints, and then the editors of the journal will find referees, using their quick opinions and more detailed reports in the usual way in order to decide which papers will be accepted.

Read the rest.


OECD: Students, Computers and Learning

This OECD Report is in news (see, for example, Too much technology ‘could lower school results’ at the BBC). What follows are some quotes from the Report related to mathematics.

The results also show no appreciable improvements in student achievement in reading, mathematics or science in the countries that had invested heavily in ICT for education. And perhaps the most disappointing finding of the report is that technology is of little help in bridging the skills divide between advantaged and disadvantaged students. Put simply, ensuring that every child attains a baseline level of proficiency in reading and mathematics seems to do more to create equal opportunities in a digital world than can be achieved by expanding or subsidising access to high-tech devices and services. (p. 3)

What the data tell us
• Resources invested in ICT for education are not linked to improved student achievement in reading, mathematics or science. […]

• Overall, the relationship between computer use at school and performance is graphically illustrated by a hill shape, which suggests that limited use of computers at school may be better than no use at all, but levels of computer use above the current OECD average are associated with significantly poorer results. (p. 146)

Continue reading

Project-Based Mathematics

Does any one know of any country, state, school which has adopted PBM as the way to teach and assess mathematics in the final two or three years of secondary school (before sixth form)? I don’t mean the use of projects to enhance the lessons or help children learn and apply concepts, but the whole three years based on projects with, say, 60% of the final assessment based on class-based project work and 40% on a written exam, for the O level.

The Secret Question (Are We Actually Good at Math?)

Posted on the AMS Blogs on September 1, 2015 by Ben Braun

“How many of you feel, deep down in your most private thoughts, that you aren’t actually any good at math? That by some miracle, you’ve managed to fake your way to this point, but you’re always at least a little worried that your secret will be revealed? That you’ll be found out?”

Over half of my students’ hands went into the air in response to my question, some shooting up decisively from eagerness, others hesitantly, gingerly, eyes glancing around to check the responses of their peers before fully extending their reach.  Self-conscious chuckling darted through the room from some students, the laughter of relief, while other students whose hands weren’t raised looked around in surprised confusion at the general response.

Preterm Birth Linked With Lower Math Abilities and Less Wealth

From: news@psychologicalscience.org
September 1, 2015
For Immediate Release
Contact: Anna Mikulak
Association for Psychological Science
amikulak >>at<< psychologicalscience.org

People who are born premature tend to accumulate less wealth as adults, and a new study suggests that this may be due to lower mathematics abilities. The findings, published in Psychological Science, a journal of the Association for Psychological Science, show that preterm birth is associated with lower academic abilities in childhood, and lower educational attainment and less wealth in adulthood
“Our findings suggest that the economic costs of preterm birth are not limited to healthcare and educational support in childhood, but extend well into adulthood,” says psychological scientist Dieter Wolke of the University of Warwick in the UK. “Together, these results suggest that the effects of prematurity via academic performance on wealth are long term, lasting into the fifth decade of life.”

Continue reading

The Quadratic Formula in Malta’s Learning Outcomes Framework

What I see as a deficiency of the Learning Outcomes Framework is that it does not specify learning outcomes in a usable way.

There are several references to quadratic equations in Levels 8–10, for example

Level 8
Number – Numerical calculations
18. I can solve quadratic equations by factorisation and by using the formula.

If a student from Malta comes to my university (and I have had students from Malta in the past, I believe), I want to know what is his/her level of understanding of the Quadratic Formula.

There are at least 7 levels of students’ competencies here, expressed by some sample quadratic equations:

(a) x2 – 3x +2 =0
(d) x2 – 1 = 0
(c) x2 – 2x +1 = 0
(d) x2 + sqrt{2}*x – 1 = 0
(e) x2 + x –  sqrt{2} = 0
(f) x2 + 1 = 0
(g) x2 + sqrt{2}*x + 1 = 0

These quadratic equations are chosen and listed according to their increasing degree of conceptual difficulty: (a) is straightforward, (b) has a missing coefficient (a serious obstacle for many students), (c) has multiple roots, (d) involves a surd, but no nested surds in the solution, (e) has nested surds in the answer, (f) has complex roots, although very innocuous ones, and (g) has trickier complex roots. Of course, another list  can be made, with approximately the same gradation of conceptual difficulty.

I would expect my potential students to be at least at level (d); but LOF tells me nothing about what I should expect from a student from Malta.

And one more comment: a comparison of the statements in the LOF Level 10:

I can solve quadratic equations by completing a square

and in the LOF Level 8:

I can solve quadratic equations by factorisation and by using the formula.

apperars to suggest that at Level 8 the Quadratic Formula is introduced to students without proof or proper propaedeutics which appear only at Level 10. In my opinion, this should raise concerns: at Level 8, this approach has a potential to degenerate into one of those “rote teaching”  practices that make children to hate mathematics for the rest of their lives.

Malta’s Learning Outcomes Framework: a Discussion

Malta’s new Learning Outcomes Framework for school mathematics is an important case study of the European Union’s approaches to implementation of its education policies in member countries. For that reason the Framework deserves a close attention.

The original post of 13 August generated more responses than it was anticipated, and it is useful to collect them all at a single page.