Education ∪ Math ∪ Technology

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My grandmother on learning how to write

My grandmother, Frances Shelley Wees, was an author and as such, she would often receive letters from people, particularly young women, asking her how she got started. A kind stranger found this letter from my grandmother to her grandmother (Mrs Hanson) in her possession, found me online, and emailed me a scanned copy of her letter. I’ve transcribed it below.

My dear Mrs. Hanson;

I hope you will forgive me for not having answered your letter long ago. We have been back in Toronto for two weeks, but I’ve been settling us in a new house and getting my youngster’s clothes ready for winter–you know exactly what it’s like, I’m sure. And the grapes and the crabapples are still in the fruit stalls here and I’ve got a very jelly-minded family so I felt I had to do my housewifely duty by them.

I wish I knew exactly how to advise you to go about writing. I do think that what might be the right procedure for one would be wrong for another. In my own case, I’m sure a course such as the Shaw Schools offer would have been the wrong thing to take at the beginning, although, I think, like you, that I might profit by it now. I don’t, of course, know how old you are; but your letter sounds so sensible and philosophic that I don’t think you can be told the things one tells the twenty-year olds when they come asking. I tell them to go home and write and write and WRITE and forget about themselves and how famous they might some day be, and scrape off all the fancy polishes and work for simplicity and humility. You’re so much beyond them in your outlook on life. Maybe a story course, which would emphasize technique and give you a few rules, would be exactly right. Before technique, I feel, comes an attitude of mind, hard to acquire but invaluable. Until one has that attitude all the courses in the world are pretty much wasted, I should think.

I don’t really know anything about the Shaw Schools. I’ve heard of Mr. McKishnie. Their price seems pretty high. There is a first class course offered by the Home Correspondence School of Springfield, Massachusetts, which is only thirty-odd dollars. I’ve seen some of the lessons and criticisms, and thought them first-rate. Perhaps you would like to write to them and get their literature. The man who is at the head of it has been operating his school for a great many years and has written several of the leading text-books on short-story technique.

You ask about how I began. It might be misleading if I say I just began, with no training–I’ve not been to University and I never took any courses of any kind–because I had a husband who was (and is) a psychologist and a writer, and a number of friends who were more than generous with help and criticism. So that I got a good deal of guidance, some of which I did not at the time particularly appreciate. I honestly think that my greatest helps were the books on criticism and technique which i got from the libraries. I suppose I have read and minutely synopsized fifty or sixty of them, and of course have read countless others. Not quite countless; there aren’t so many. Perhaps you could get them through the extension library of your University (I’m not sure Saskatchewan has an extension service, has it? If not, you might try Alberta. Miss Jessie Montgomery, Extension Library, U.ofA. would do whatever she could for you, I know. She would send you a list of such books and if the regulations permitted would send the books themselves if you would pay the postage.

You have a number of advantages as a beginning writer, and your place of residence being one of the greatest. I find it much more difficult to write in the shut myself away for the long periods of time necessary to do a good piece of creative work. Of course I enjoy all the interesting things going on about me, and eventually find them stimulating; but while I’m writing, all the stirring about me is irritating. I wrote my first five books in a little town in Alberta where I had my friends all warned that if they dared ring the telephone between certain hours I would put the curse on them.

I feel that this is a very inadequate letter, Mrs. Hanson, and I wish I could do something that would really help you. I know so well those early helpless feelings, the blackness of not knowing where to turn and yet having to go forward. I wish I could ask you to send something you’ve written for me to criticize, but time is a thing I don’t possess. Criticism is the thing beginners need most, I suppose. Although I’m not even sure about that. Maybe all they need is the firm resolution to be honest with themselves, to find out what they truly feel and believe about life and people then to write as simply as possible. If I were you I should most certainly attempt to sell the poems. You might try SATURDAY NIGHT, here in Toronto. You might try the Saskatoon paper, or any of the other western papers which use poetry. Get something into print as soon as possible. Seeing it there will open a strange and rather terrifying door for you…but the sooner that door is opened, the better.

Do send me a little note some time to say how you’re getting on. Thank you so much for your good wishes…I need them. I don’t find the path any too smooth. I don’t think a women does, when she has to manage a house and take care of a family. And there’s never as much money in writing as people think there is, not enough for the first years anyway to pay for responsible assistance. You have to mend socks with one hand and type manuscripts with the other, and carry whooping cough along in the next compartment to The Great Canadian Novel..and you have to like it.


Frances Wees


Here are the big messages I see in my grandmother’s advice to this young writer:

  1. To improve as a writer, WRITE,
  2. Simple writing is more effective,
  3. Attitude is critical, more important than knowledge,
  4. Knowing the mechanics of writing is important as well, and you can learn these on your own,
  5. Guidance and criticism is valuable, but so is self-criticism and self-learning,
  6. Solitude and the ability to work in peace and some isolation is important,
  7. Having an audience matters, and the sooner one has an audience, the better,
  8. Space and time to write is helpful, but clearly not essential. Desire is essential.

Research on word processors in student writing

I was looking for research on whether word processors are effective when students are learning to write. So far the research is supportive, but I can’t find any research done recently. I suspect there must be research that is current and supports students using word processors. Please let me know if you have any research more recent than what I have below.


Bangert-Drowns, R., (1993). The Word Processor as an Instructional Tool: A Meta-Analysis of Word Processing in Writing Instruction, Review of Educational Research, p69-93, doi:10.3102/00346543063001069

Abstract: Word processing in writing instruction may provide lasting educational benefits to users because it encourages a fluid conceptualization of text and frees the writer from mechanical concerns. This meta-analysis reviews 32 studies that compared two groups of students receiving identical writing instruction but allowed only one group to use word processing for writing assignments. Word processing groups, especially weaker writers, improved the quality of their writing. Word processing students wrote longer documents but did not have more positive attitudes toward writing. More effective uses of word processing as an instructional tool might include adapting instruction to software strengths and adding metacognitive prompts to the writing program.

Lewis, R., Ashton, T., Haapa, B., Kieley, C., Fielden, C., (1999). Improving the Writing Skills of Students with Learning Disabilities: Are Word Processors with Spelling and Grammar Checkers Useful?, Learning Disabilities: A Multidisciplinary Journal, retrieved from on May 22nd.

Abstract: A study involving 106 elementary and secondary students with learning disabilities and 97 typical peers found that students who used spelling and grammar checkers were more successful than transition group students in reducing mechanical errors, particularly non-real-word spelling errors, and in making positive changes from first to final drafts.

Owston, R., Murphy, S., Wideman, H., (1992). The Effects of Word Processing on Students’ Writing Quality and Revision Strategies, Research in the Teaching of English, Vol. 26, No. 3 (Oct., 1992), pp. 249-276

Abstract: This study examines the influence of word processing on the writing quality and revision strategies of eighth-grade students who were experienced computer users. Students were asked to compose two expository papers on similar topics, one paper using the computer and the other by and, in a counterbalanced repeated measures research design. When students were writing on the computer, "electronic videos” were taken of a subsample of students using an unobtrusive screen-recording software utility that provided running accounts of all actions taken on the com- puter. Papers written on computer were rated significantly higher by trained raters on all four dimensions of a holistic/analytic writing assessment scale. Analysis of the screen recording data revealed that students were more apt to make microstructural rather than macrostructural changes to their work and that they continuously revised at all stages of their writing (although most revision took place at the initial drafting stage). While the reason for the higher ratings of the computer-written papers was not entirely clear, student experience in writing with computers and the facilitative environment provided by the computer graphical interface were considered to be mediating factors.


Student brings typewriter to class

Youtube video link

In this video, shared with me by Philip Moscovitch, a student has brought a type-writer into class. Is this perhaps, as Philip suggested, a protest against the use of an old pedagogy by bringing in an old technology? Does the use of a typewriter to record notes seem a bit ridiculous? Is it even more ridiculous that the student, as he states at the end of the video, can download the notes for the course?

A well motivated, literate student can learn as much or more from a good set of notes (or a decent textbook) for a course. Why come to class at all if all that is going to happen is a repetition of the notes?


Scientific method

Science lab
(Image credit: Jack Amick)


When many people think of science, they think of the tools of science, much like the photo of a traditional science lab above shows. They think of beakers, and hypotheses, and labs, and think that this is science. Playing with the tools of scientists does not make one a scientist, or become a scientist. Thinking like a scientist does.

Science is a way of thinking, a way of reasoning about the world. People who reject science, reject reason. Science is not a linear process, it is a dynamic way of thinking and collaborating about the world.

There are flaws with this way of thinking, as there are with all ways of knowing. Science cannot answer ethical questions. Scientific results get fabricated, exaggerated, and misunderstood all the time, since they are produced and understood by human beings. However, the process of reproducing results with additional experiments ensures that, over time, bad ideas get weeded out of what we know to be true about the world. Ideas which are correct get re-inforced by additional experiments.

Teaching science as a series of facts someone else has discovered about the world does not give them the opportunity to learn about the process through which those "facts" were discovered. The process, in this case, is far more important than the result. Our schools need to spend far more time dealing the messiness of the process of science, and less time focusing on the results of the scientific process. Students learn process through practicing it.

We also need to recognize that the standard science lab write-up emphasizes a linear process of science, which does not exist anywhere in the scientific community. Following someone else’s lab to learn how to use the tools of science is fine, but one must actually design experiments for oneself in order to learn the process. We need to de-sitcom science education.

Toxins in schools

No peanuts allowed
(Image credit: Schockwellenreiter)

It occured to me today that schools spend an enormous amount of effort to ensure that they are free of toxins for students. We ban common allergens from the school that are life-threatening for some students (like peanuts) and we build our schools so they do not contain asbestos insulation or lead pipes. Some schools are very concerned about the effects of wifi on students, and so have banned wifi from their schools. When we have a belief as a community that something is toxic for our students, schools rally to protect students from that toxin.

So why are so many schools toxic places for LGBTQ youth?

Obviously many schools have made an effort to develop cultures which are supportive of all of their students, but there are places where physical toxins are banned, and emotional ones are encouraged and even nurtured.

Teaching probability

My colleague found an activity to do with his 5th grade class, similar to this one. Basically, he gave the students 10 coins each, and asked them to put the 10 coins on a number line (with numbers from 1 to 12) with a partner. Each round they roll 2 six-sided dice, find the total, and remove a coin from their number line if it matches the roll. They keep going until one of the two students has no coins on the number line.


At first, most student’s starting positions looked like this:

Student 1 - flat distribution

or this:

Student 2 - another flat distribution


At the end of the lesson, we played a 5 coin version of the game, and one student’s paper (after 1 round) looked like this:

Student 3 - All 4 coins on number 7


Unfortunately, although most of the students did notice that some numbers came up more frequently than others, as evident by their distributions looking a bit less flat, and bit more centred on 7 on the number line, many of the students still had obvious misconceptions of probabilty. Students made comments like:

"If I spin around twice before rolling, I get a more lucky roll."

"I got a few 11s last game, so I’m going to put a few more coins on 11."

"8 is my lucky number! I’m going to put 3 coins on 8."

"I need to spread out my numbers so I have more chance of getting a coin taken on each roll."

Our plan for next class is to have students switch up groups, discuss insights they’ve had on the game, play a couple of rounds, switch them up again, while we walk around and see what strategies they use. Hopefully we’ll see less students spinning around in order to improve their dice luck…

I also asked for resources on Twitter for using a probability game as part of a lesson on probability, and had the following 5 games recommended (all of these look good because they are relatively easily produced and used in an elementary school classroom).



I wrote a simulation to test to see what distribution of coins is the best. I am somewhat surprised by the results. Check it out here.

Why am I surprised by the results? My intuition about how this game works failed me. I thought that the likelihood of each number coming up was the most important factor in deciding a good strategy for the game. It turns out that one has to balance out the knowledge of the likelihood of each number being rolled with having a selection of numbers available. It may be that the probability of a 7 being rolled is 6/36 but the probability of a 6 or a 7 being rolled is 11/36.

In fact, it turns out that having a selection of different rolls available is fairly important. I updated the simulation so I could choose the number of coins to place, and with 3 coins placed, choosing 4, 5, 6 is better than having all three coins on the number 7.  With 2 coins, it is better to choose 6 and 8 than to put both of the coins on 7 (although 6, 7 is better than 6, 8 – but only slightly).

There are three messages I get from running this simulation.

  1. One should, in general, not make too many intuitive assumptions about how probability works, particularly with somewhat complicated examples.
  2. One should be careful how one uses even simple games to teach probability. All of the students saw that 7 was the most common number, but their intuition of "choosing a wide spread" is a valuable one for this game, but it doesn’t help us get at the idea of some numbers being more likely than others. I think we’d need a different game for that.
  3. It is probably a good idea to build the simulation before you play the game with students, if at all possible.

PISA results from 2000 to 2009 for Canada

I noticed through this blog, that the CBC had published the PISA results for Manitoba (released as charts) for 2000, 2003, 2006, and 2009. I wanted to verify the results they had posted, especially the mathematics data, so I went and looked up the data for myself on the Stats Canada website (which you can access yourself here, here, here, and here). Using this data, I created th graph below, which shows the scores in math for Canada and for each province (get the raw data here).

I’m not sure what this data shows, although I can see some trends. Of course, if I change the scale, the overall trend seems more clear.

It looks to me like overall the results have been somewhat stable, at least at this scale. While the trend in Manitoba definitely looks like a downward turn for the last few years, and this trend is probably statistically significant, overall for Canada, it looks like the results have moved somewhat randomly, as one would expect from year to year.

Culture and counting

Not convinced that there are cultural nuances in how we understand and define math? Watch the following short video (see for the source) in which a child explains the number system his culture uses to another child.



There are other areas in which we understand mathematical concepts differently depending on our culture. For example, this recent study suggests that something like ‘numbers come in a certain order’ may be a cultural representation, and not one of which most of us are aware.

One wonders, if we can see such dramatic differences between different cultures in terms of understanding something fundamental like number, how likely is it that there are other differences within our own culture?

My wife, for example, tends to rely on landmarks for navigation, but I tend to rely on an internal map based on the names and numbers of the roads. She and I therefore have a different understanding of how one should navigate. I can remember meeting people who could not read a map (but who were otherwise able to navigate with ease) suggesting that our representations of geographical information may differ greatly between different people.

How does this influence how we should teach?

We didn’t do any math yesterday

Practice makes perfect comic


Yesterday, I was covering a colleague’s math class at the last minute, and he had made photocopies of a chapter 1 to 7 review. I looked at the review sheets, and the grade 10 students in front of me, and decided that it was unlikely that the review sheets were going to be useful. I handed them out, and then started putting puzzles up on the board.


Seven Bridges problem

The first puzzle I put up was the Seven Bridges of Königsberg problem. Within  a couple of minutes, every student was trying to figure out the path across the 7 bridges that doesn’t cross any of the bridges more than once. Before the students got completely frustrated with this problem (since it is deceptively simple to state, but "difficult" to solve), I put up a couple more problems, including a gem from Dr. Gordon Hamilton. I added the frog hopping problem to the board, and taught two students the game of Nim.

Each problem had some students who were working on it intensely. Every student found some problem which was interesting to them, and almost all students were working in small groups on the problems and puzzles. Eventually, a small group of students gave up on all of the puzzles and worked on the review sheets while the rest of the students continued to work on the puzzles until the end of class.

Some students asked for a hint on the bridge problem, and I led them (through questioning) to Euler’s formulation of graph theory. From this, we discussed that there could be at most one starting spot, and one ending spot, and that only a starting and ending spot could have an odd number of paths leading in and out of it. I then put up the 5 rooms puzzle, which one of the girls said within seconds was unsolveable by applying Euler’s analysis to the graph.

A group of boys worked on the frog problem, and went from struggling to even find a single solution to the 3 frog problem to being able to generalize a solution for n-frogs on either side (and a formula for determining the number of moves for each frog puzzle).

The next day, I spoke to my colleague, and asked him if he was okay that I had not done the worksheet with the students. As expected, he was fine with it. I asked him what the students said. He said that students said that they enjoyed the day before, but one student had said, "We didn’t even do any math yesterday."

I’m not sure I agree with that student, and I’m slightly distressed that he didn’t see the problem solving activities we did as being part of math. What do you think? Are problems like these important in mathematics? If so, why aren’t more of them in our curriculum?

Interesting ways to use Google Apps in the math classroom

I just found this presentation from more than a year ago on some interesting ways to use Google Apps in a mathematics classroom. I noticed that it had been edited slightly, so I did some more edits and thought I would share it here.

You can help edit and curate it here. I could imagine that Google+ would be useful, and that some of the file sharing options through Google Drive have improved, neither of which has made it into this presentation yet.