Education ∪ Math ∪ Technology

Year: 2012 (page 7 of 14)

Why people often do not accept the research

Via the @BCAMT email list-serve:
 

"[T]here is an interesting (and disturbing) literature on situations in which information does not change prior biases or decisions. The word I have seen is ‘motivated reasoning’.

Interestingly, I ran into a problem of ‘motivated reasoning’ with a class of future teachers. The question is: when would research about the teaching and learning of mathematics change their classroom practices. A common response to articles, given some practice in critiquing research, was:\

– if I agree with the conclusion, the article was reliable;
– if I disagree with the conclusion, then here are x reasons why the article was not reliable and I should not change my practices!" 

Dr. Walter Whiteley


Dr. Whiteley works with pre-service teachers, and would like me to point out that they are still in the middle of articulating their own personal theories of how learning and education work, thus they lack experience in schools from the other side of the desk. It is therefore possible that this is an issue isolated to pre-service teachers.

On the other hand, I have seen people vehemently defending a position that has no merit simply because they are unwilling (or unable) to see that the evidence is mounted against them. I have also noticed many times that months later, this person has changed their perspective, sometimes claiming that the opposite to what they had previously believed was their belief the whole time, so maybe that argument influences their thinking later, and they are more willing to change on their own.

It takes enormous strength of will to remind ourselves of our cognitive biases, and act against our instinct to defend our mistakes. I can’t say I’ve succeeded at this all that much. Does anyone?

 

Imagine something different

See this piece of paper?

Piece of lined paper
(Image credit: D Sharon Pruitt)

 

Throw it away.

Imagine the limitations of the piece of paper shown above do not influence how you share the record of learning your students have done, with their parents, and the wider community.

Now remember the history of grading, which started with one William Farish (in Western culture – Chinese culture has been apparently giving grades to students for many centuries for the purpose of sorting their children into social classes.). William Farish (re)invented grades as a way to increase the number of students he could "teach’ for the purposes of lining his pockets (at the time, more students meant more money).

What would you do differently to share your student’s evidence of learning, if the limitations of the paper above did not exist, and if your purpose was neither to sort students into social classes or line your pockets by being able to teach more students? 

Looking for feedback on this puzzle game

I’m working on a block puzzle game. The objective is to cover the entire puzzle area with blocks of various sizes. So far I’ve got the basic structure up (it will only run in web browsers that support the Canvas HTML element, so Safari, Firefox, Google Chrome, and maybe Opera). Scoring for the game depends on what types of blocks are used (you’ll notice those little 1 by 1 squares are worth no points).

I’m looking for feedback on how to improve the puzzles.

https://davidwees.com/javascript/blockgame/

Some ideas I’ve had are:

  • Restrict what playing pieces the players can use.
  • Randomize the playing pieces to which the players have access.
  • Allow more access to different kinds of shapes, such as triangles, pentiminoes, heximinoes, etc…

 

Update:

Here is some feedback I’ve received as well from other sources.

  • Change the images that turn into the blocks into pictures of the blocks. @joshgiesbrecht
  • Change from scoring blocks to a par system (like golf) where players get scored on the number of blocks used. @joshgiesbrecht
  • Make the point that one gets a higher score from using larger pieces more obvious. @joshgiesbrecht

An Unfamiliar Revolution in Learning

This video, shared via the Good blog is a must watch. Find six and a half minutes to watch this video, and ask yourself what changes would be necessary in your school to make it more like this one.

 

The work that this school does on teaching empathy, and understanding what it feels like to be another person, is an incredibly valuable life-skill. The abstract reasoning that one gains as one learns empathy has to have side-benefits for academic reasoning as well. If I know what it feels like to be you, and what you likely feel like, I may be able to better make predictions about other types of objects in the world as well.

I particularly like the five habits of mind the school has used for their conceptual framework:

  • Evidence – How do you know?
  • Conjecture – What if things were different?
  • Connections – What does it remind you of?
  • Relevance – Is it important? Does it matter?
  • Viewpoint – What would someone else say? How would someone else feel?

 

Nobody remembers names

Almost everyone I meet tells me when I first introduce myself that they are horrible at remembering names. I am patient with them and am happy to repeat my name for this person several times.

Why should we expect someone to remember our name the first time? It’s essentially a random piece of information which has no relationship to who we are as people. We learn names by immersion (other people around use the name), by repetition, in context, and by using the name ourselves.

So why would we expect our students to remember disconnected facts without immersion, repetition, context, or use?

Annie Fetter on the development of math teachers

 

Annie gives a very short talk that highlights some of the issues in math education, and which I can tie to work various people have done on learning.

Everyone who is trained to become an educator has some fairly strong intuitive sense of what it means to be an educator. They have seen educators work, and they know how to copy the behaviours of the teachers they have seen. Unfortunately, often we want to change teachers behaviours, and so we must address the misconceptions that teachers have about learning head-on.

If you do not address the misconceptions that people have, chances are very good that they will incorporate the new information you present (in almost anyway that you present it) into their existing misconceptions and as a result, not change their behaviours at all. This is a problem that numerous educators have discovered (it seems independently of each other) and one which definitely has implications for teacher education.

Annie’s observation that her teaching college in 1988 was already talking about inquiry based learning, and some pretty serious reforms in mathematics education, and then her description of her beginning practices which were so different, gets at the heart of this issue. She was "taught" that inquiry based mathematics is an effective pedagogy, but she didn’t hear it. She probably did hear it, but she thought that her notion of what inquiry based education meant was the same as what she was doing. She was unable as a beginning teacher to see how different her techniques were than what she was being taught to do.

So if we want to change teacher education, we definitely need to assume that the student teachers coming in have an understanding of what it is to teach, and that much of what they understand is misguided and just plain wrong, and we need to incorporate the wrongness of this approach into our instruction of teachers.

Multidisciplinary projects in schools

It is my experience that we compartmentalize knowledge entirely too often in schools, labelling some ways of learning mathematics, other ways of knowing science, and still other ways of knowing the humanities. We compartmentalize knowledge so much in schools that I believe it leads to what I like to call Sitcom teaching, in which each lesson is a stand alone that does not depend on any other subject areas (or often even the previous lessons in the same class) in order to be learned by students. 

This is a dangerous practice because it leads students to believe that mathematical thinking is somehow incredibly distinct from other types of thinking and to the logical conclusion that they can get by in life without being able to reason mathematically, or that it is even possible to live life without using mathematical reasoning. This is clearly false – the similarity between what we think of as different modes of thinking is much more than the differences. Just thinking of similarities and differences as I have pointed out in the previous sentence, a common activity in the social sciences, is using the basic ideas inherent in mathematical set theory. 

A potential cure for compartmentalization is multidisciplinary learning, wherein the skills, knowledge, and modes of thinking are rejoined together to form whole projects.

Here are some sample multidisciplinary projects:

  • Build a community garden

    In this project, students could learn science as they observe how the plants grow, and be encouraged to experiment with different amounts of light, watering, fertilizer, and soil preparation techniques to see how these variables affect plant growth. Younger students can count out seeds, and work with older children who help them carefully arrange these seeds into rows and columns. Students could learn how to calculate the lengths of shadows during the course of a day, and thus work out where are the best places for Tomatoes in their garden. Students could write letters of invitation to various community organizations to invite them to use the community garden. They could write grant applications to seek funding for their garden and petition local businesses to offer financial support for the garden. They could research how farming practices have changed over time. They could learn about the environmental consequences of our global food supply.

    At the end of the season, they could harvest and cook their own food. They could give away the food to a local food bank. 
     

  • Run a store

    Students could create budgets, order supplies, and keep track of inventory. They could research the health benefits (and problems) associated with various kinds of food. They could write proposals to change inventory selection. They could read about the manufacturing process for the goods in their store, and write letters to the manufacturers either requesting more information or a change in harmful practices. They could use their experiences in the store as a background for a short story. They could sell their art work, or books of their poetry. They could donate the proceeds to charity, or use them to buy supplies for their school.


  •  Create an (rock) opera

    Writing musical scores would let students learn more about fractions, sequences, and counting. Students could research different musical styles, and learn more about their culture. Students could create the music, the stage settings, design the costumes, program the lighting sequence, and create the program booklet for the performance night. Students could create multiple storylines and then find ways to bring their ideas together (where possible).

 

Of course, there are a lot of other project ideas not listed here. To implement these in most current school settings, teachers would have to collaborate and work together fairly well, and we might have to set aside some of our standard school schedules. However, we should never let the school schedule have too much control over the kinds of learning activities we do with our students.

What other benefits do you see to this approach? What are the problems with it?

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 city..to 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.

Sincerely,

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.

Parent questions about technology

A parent today told me how much she enjoyed the session I had with parents about technology use last year, and said that she had talked about the session with a group of parents from the school.

She said it would be wonderful if I could do it again, but she also thought parents may not be able to attend because they would be too busy.

I had the thought that creating a blog could help with this issue. One could start by presenting some common questions parents have, and/or a short video response/presentation by someone knowledgeable in the field. Parents could discuss the issue further in the comments, ask more questions, and debate whether the response by the technology "expert" is in fact reasonable. Some entries could be nothing more than an image or video and some questions to debate in the comments.

It seems to me that many parents would have questions about technology use, and that constructing a common platform for many of us to use would be helpful. We all have parents who ask questions about technology, and although we would like to pretend we have the answer, we don’t always do.

Here are some sample questions that I have heard parents ask:

  • Is wifi safe?
  • Should I allow my child to play computer games?
  • Is social media safe? What is social media, anyway?

I’ve started a blog, which I call "Questions About Technology" (link may not be active for you for up to another 48 hours) I’d like to invite interested parties to join me.