Understanding the Mathematics using English

For language-minority students, mathematics classrooms based on inquiry and problem solving hold particular promise and challenge. Conversation permeates both scientific research and the solution of mathematical puzzles. This talk takes the form of asking, describing, explaining, hypothesizing, disputing, clarifying, elaborating, and validating findings.

Although there are considerable language requirements, there is a good chance that pupils will master both scientific and math concepts and crucial English language phrases.

Mathematics has long been considered a subject with little linguistic need. Language actually helps mathematical reasoning, thus mathematics and language are closely related. Students today need to be proficient in applying at least the fundamentals of mathematics because of the focus on problem solving and communication in mathematics. The terminology and discourse structures used in mathematics are specialized. Additionally, words like equal, rational, irrational, column, and table that have different meaning in mathematics are included.

There are several methods to signal mathematical processes, which presents extra difficulties for pupils from linguistic minority backgrounds. For instance, the phrases add, plus, combine, and, total, enhanced by, can be used to denote addition. There are several mathematical symbols that are utilized differently in other nations than they are in the United States. For instance, commas can be used to divide whole integers and decimal parts (functioning as the decimal point does in this country). On the other hand, a decimal point may be used instead of the comma to distinguish hundreds from thousands, hundred thousands from millions, and so on.

Students who speak a language other than English may try to read and write mathematical phrases in the same manner that they read and write regular narrative prose. They could attempt to translate verbatim between a mathematical notion described in words and a mathematical concept written in symbols, in other words. But the order in which a mathematical notion is conveyed in words frequently differs from the order in which it is expressed in symbols. Most of the time, a linear, one-to-one translation is not feasible.

The collaborative aspect of scientific discourse is acknowledged in science as being a highly communicative field where language plays a key role. There is, however, a recognized style of “talking science.” Language norms may be seen in the ways that scientists argue or disagree, present hypotheses or express findings, and negotiate meaning by expanding, paraphrasing, or asking clarifying questions.Particularly younger students learning English as a second language can have trouble comprehending the relevance of logical inferences made in scientific and mathematical discourse.  Logical connectors are words or phrases that indicate a logical link between different parts of a text, such as the terms if, because, nevertheless, and therefore. Logical connectors are symbols used in mathematics and science to denote similarity or contradiction, cause and effect, cause and effect, reason and outcome, and chronological or logical succession. Restating a mathematical or scientific problem as a declarative phrase may help students who struggle with logical linkages to find an answer.

Teaching Online

Online learning, like any instructional modalities, has its own set of advantages and disadvantages.

Online courses are often not as successful as in-person classes, but they are obviously preferable than none at all.

Many online learning systems have recently emerged for a variety of reasons, such as LiveXP for teaching new languages, Cuemath for teaching mathematics, and so on. When I’m working with pupils, I utilize Google Meet.

One of the most difficult aspects of online learning for many students is the inability to concentrate on a screen for lengthy periods of time.

Despite all of the drawbacks of online education, I believe it is a really promising field of study.


Nice photos from NASA in the Boston Globe with captions.

Moondust by Andrew Smith is worth reading, despite the review, because its the only account of the thoughts and reflections of those who walked on the Moon that is easily available. The author felt a need to put Project Apollo into the context of his life (at some length, alas). I suspect all of us alive as children then will tend to associate the landing with childhood memories and culture. I think it is the result of this immense technological effort being experienced in child size pictures on black and white tellies.

twitter for essays

Twitter includes a 140 character limit on each twit. Sounds like an ideal constraint to me. Challenge to students: summarise today’s lesson in one twit. Provide a copy of the blank above to each student…

Paul Constant has written a review of twitter as a series of twitter posts (via daringfireball.net). Now, what I want to get going is a short story told by 5 to 7 twitterers taking turns…

…as anyone who has looked at my twitter page will have guessed, I’m using twitter simply as a way of saying where I am each day. I’ll try a bit of the location specific writing over the holiday. Photos on flickr.

An unusual application of fractions

Image detail taken from a scan of a notebook opening on Kyle Gann’s Post Classic blog.

I’m just beginning to replan my teaching of fractions… I’ll have to get some simple music examples in there somewhere.

Mobile Broadband Coverage

OFCOM have published comparative maps of mobile broadband coverage (Jan 2009) showing various providers for the UK.

t-mobile 3G above…

3G coverage.

No brainer, if you live in Scotland, you need a wired connection. What surprised me was the fractal holes in the Birmingham conurbation area on t-mobile (my current web’n’walk modem) and the contrast with 3G, the best provider nationally.

The Register chronicles the difficult process by which these large scale maps were made public. I want a Web site I can pop a postcode in and get coverage maps down to antenna level. I want an efficient market.

I find it really quaint that I can use a modem dial script with a USB modem in a minimal linux install on a flea powered web book. AT Hayes codes in a terminal window… bosting

Copyright free images

Image*After and MorgueFile are Web resources where you can find and download high resolution photos for use in PowerPoint presentations or Web pages. MorgueFile’s name comes from the archives kept by newspapers and the Police of old photographs. You can used the ‘advanced’ search page in Flickr and specify only images with a Creative Commons licence.

Remember Seth Godin’s Really Bad PowerPoint e-book?

“You put up a slide. It triggers an emotional reaction in the audience. They sit up and want to know what you’re going to say that fits in with that image. Then, if you do it right, every time they think of what you said, they’ll see the image (and vice versa).1”

I’d use the image above if I was doing a presentation about how newspapers are failing to react to the Web and the new advertising models. The old press with swarf on the cogs and dull metal rollers conjures up the smell of the presses (I used to walk past the Liverpool Echo presses most days 30 years ago) and conveys the oldness of the medium. I’d need other images to show what is being lost as the newspapers drain money and eyeballs.

It doesn’t matter

“… why am I completely incapable of putting non-verbal marks on a page so they do the same? What neural channels are so blocked that my ducks don’t just look wonky, they look like scribbles? Why does eye-mind-hand work about as well in me as I contemplate a teacup or imagine a tree, as it does in my two-year-old nephew?”


“This must be what a lot of real beginner-writers feel. There’s stuff in their head or before their eyes which they yearn/burn to get down on paper. And when they try? It reads like scribbling. Awkward, ugly, incompetent, even incomprehensible. The one writerly skill I’ve always had is the capacity to bend words to my purpose (I just had to learn everything else about writing fiction). So I’ve never really had the feeling that the words in my hands won’t do what my mind wants them to. Now by analogy I know how it feels, and as a teacher that’s a lesson worth its weight in red biros.”.

Emma Darwin, It doesn’t matter

All teachers should have something they do that ‘doesn’t matter’ and that they have to learn from scratch. That’s me and my piano, Darwin and her drawing. Then we can understand students better. What’s your thing that does not matter?

Is Google making us Stupid or Smarter?

Two articles from The Atlantic

  • Is Google Making Us Stupid by Nicholas Carr
  • Get Smarter by Jamais Cascio

Both reference Proust and the Squid by Maryanne Wolf.

Chrome OS and toasters

Computers should be like toasters, they should just work for years and then when they stop working, you should be able to pop out and buy a new one. Toasters don’t need backups, and a major cause of problems with computers is loosing data (which may include family pictures and purchased music as well as College work).

Google’s Chrome OS looks like it might be a solution to both failing PCs and the need to back up data. It will be the second branded operating system built on top of an open source kernel and tool chain. Mac OS ‘just works’ and looks nice, has full desktop functionality, local storage and a huge range of software. By contrast (BBC report, Google) Chrome OS may not be able to run applications that require an API richer than the browser. The obvious questions that spring to mind include “Where do I keep my music/photos/videos?” and “What happens if my Internet connection fails?” and “How do I install real programs?”. Local storage with cheap online backup could be a very popular combination. The gOS operating system had direct links to Google Apps integrated into a nice desktop, but used local storage and had OpenOffice installed.

Google mention working with hardware manufacturers. My toaster PC in the photo above is the Aleutia E2, a low power fanless PC that has enough processing power to view Web pages, do e-mail, write Maths worksheets and presentations, but does not quite make it through a YouTube video. That runs Debian Squeeze, but there is a spare partition, and I’ll be trying the Chrome OS when it arrives in public beta form.

The Google blog carries an interesting post written just after the Chrome OS announcement that describes SMS based access to Google services in Uganda. The mobile phone may be a mass platform in many countries.

Added 11th July: A Daringfireball article has some ideas and links about Chrome OS. I think this article makes valid points. Disclaimer: I use Ubuntu and therefore according to Gruber I’m not a real person. Help, I’m fading away!