Education ∪ Math ∪ Technology

Month: March 2011 (page 2 of 2)

Lecture – from a student’s perspective

What does your classroom lecture look like from a student’s perspective? I had my students video tape my lesson from a few different places in the room, and I’ve created these videos to demonstrate what it might be like for students with various learning differences. I’m by no means an expert in this area, but I want to add another perspective on why classroom lecture might not be the best pedagogical tool.





(Thanks to @marynabadenhors for the translation!)

Can you think of what class might be like for these learners? Are there other types of learners that might suffer in a one-style-fits-all classroom? 

Female educational theorists

I asked a really stupid question, and as the list of responses and suggestions came in, I started to feel more and more embarrassed. My question was, who are the female educational theorists. In my head, I was thinking of Dewey,  Piaget, Gardner, Gatto, Holt, Friero, and other male educational theorists and wondering where all the women were.

The problem of course is that there are lots of female educational theorists but I over-looked all of them. The reason why? Sexism. Yep, I admit it, I had a sexist moment and for some reason didn’t connect what these marvelous women do with educational theory. How that is a reasonable thing to do, I don’t know, and I feel ashamed and embarrassed.

In no particular order, here are some examples of female educational theorists, all of whom are inspirations in their field.

  • Diane Ravitch (@DianeRavitch) wrote The Death and Life of the Great American School System and many other articles and publications. She tours the US doing speaking engagements.
  • Deborah Meier (@DebMeier) wrote Playing for keeps: Life and learning on a public school playground. She tours the world talking about education.
  • Linda Darling-Hammond teaches at Stanford University and her various publications are available to read here.
  • Melahnie McBride (@melaniemcbride) "is a Canadian educator, researcher and writer focused on situated emergent learning, transmedia and affinity culture in virtual environments and gaming spaces." (from her website)
  • Mary Ann Reilly (@maryannreilly) wrote Deepening Literacy Learning; Art and Literature Engagements in K-8 Classrooms and is also a photographer and educational researcher.
  • Clare Brett is a faculty member at the Ontario Institute for Studies in Education (OISE). Her research "lie[s] in the areas of teaching and learning in online and distance contexts; the social and cultural implications of technology use and the affordances of online environments for learning." (from her website)
  • Marlene Scardamalia is a researcher at OISE and is also the director of the Institute for Knowledge Innovation and Technology.
  • Jean Lave "is a social anthropologist with a strong interest in social theory. Much of her ethnographically-based research concentrates on the re-conceiving of learning, learners, and everyday life in terms of social practice." (from her faculty profile)
  • Brigid Barron researches about ways "to advance scientific understanding of social aspects of learning while contributing to the design of learning environments that lead to high levels of engagement in subject matter for all learners in educational systems." (from her faculty profile).
  • Ricki Goldman is "Professor & Director of the Digital Media Design for Learning Program & the Educational Communication & Technology Program at NYU." (from her faculty profile)
  • Sherry Turkle "is Abby Rockefeller Mauzé Professor of the Social Studies of Science and Technology in the Program in Science, Technology, and Society at MIT and the founder (2001) and current director of the MIT Initiative on Technology and Self." (from her faculty profile)
  • Amy Bruckman is an Associate Professor at the College of Computing at Georgia Tech and does research on "applying the constructivist philosophy of education to online communities." (from her faculty profile)
  • Margaret Mead introduced the idea of culture into education, suggesting that you can’t teach students without either appealing to their culture or recognizing its value.
  • Maria Montessori developed a method for teaching children by giving them self-direction in their learning, and the freedom to choose their own activities. For more information, see the Wikipedia article.
  • C. Steinkuelher "investigates the intellectual work that goes on within such games and the cultures of participation that emerge both within their virtual worlds (between login & logoff) and beyond (in the online fandom spaces around them)." (from her faculty page)
  • Lillian Katz wrote the book "Engaging student’s minds" and "is a Professor Emerita of early childhood education at the University of Illinois at Urbana-Champaign, where she is also principal investigator for the Illinois Early Learning Project,[1] a contributor to the Early Childhood and Parenting Collaborative, and editor of the first on-line peer-reviewed early-childhood journal, Early Childhood Research & Practice." (from a Wikipedia article)
  • Shirley R. Steinberg is an Associate Professor and "is the co-founder and director of The Paulo and Nita Freire International Project for Critical Pedagogy." (from her faculty page)
  • Nel Noddings "is an American feminist, educationalist, and philosopher best known for her work in philosophy of education, educational theory, and ethics of care." (from her entry on Wikipedia)
  • Maxine Greene founded the Maxine Greene foundation which "directs its primary attention to the intersections among various modes of social action and engagements with the arts. Social imagination most often finds expression in diverse art forms: film, literature, theatre, and dance." (according to the Foundation’s about page)
  • Madeleine Grumet "is a professor in the School of Education and in the Department of Communication Studies in the College of Arts and Sciences." (from her faculty page)
  • Sheryl Nussbaum-Beach (@snbeach) "is a 20-year educator who has been a classroom teacher, technology coach, charter school principal, district administrator, university instructor and digital learning consultant. She is also CEO and co-founder of Powerful Learning Practice, an organization dedicated to empowering schools and districts from across the world to re-envision their learning cultures and communities." (from her website)
  • Angela Maiers (@AngelaMaiers) "is the founder and President of Maiers Education Services, a consulting firm headquartered in Clive, Iowa. Her company provides just-in-time consultation services to schools, organizations, and individuals seeking to use technology and social media to leverage human capital and production goals." (from her website)
  • Cynthia Chambers "is a mother and grandmother — as well as a writer — and a Professor of Education. She teaches curriculum studies, research methods, language, literacy and indigenous education to pre-service teachers and graduate students." (from her faculty page)
  • Cathy Vatterott is "an education professor at University of Missouri-St. Louis who has been researching, writing, and speaking about homework for the last several years. [She has published] Rethinking Homework: Best practices that support diverse needs." (from her website)
  • danah boyd (@zephoria) is "a researcher at Microsoft Research New England and a Fellow at the Harvard Berkman Center for Internet and Society."(from her website)

We need to come up with a more compelling why

Thank you to @gcouros, @shannoninottawa and @stephen_hurley for sharing this fantastic TED talk with us on Twitter. It is definitely worth the watch.

So how does this talk apply to education? 

There is a growing group of educators who believe that there is a problem with the US education system. There is also a growing group of people who are not educators who believe there is a problem. The US public, caught in the middle, has to make a choice between these two groups since the message they are sending out is quite different.

One group believes that students deserve good schools with good teachers, and that the best way to accomplish this is by making teachers more accountable for what they do, and applying free market philosophies to both schools as a whole, and specifically to teachers. The invisible hand of Adam Smith’s economic model will force schools into innovation and improvement, provided we remove the barriers of unionization and past "bad" contracts from schools. Merit pay will allow teachers to work harder to achieve better goals for students, and Race to the Top will make states compete for money, which will force them into a marketplace of a kind.

The other group believes that schools are becoming overly regimented and that there are too many rules on how they are supposed to be run, and too many accountability measures. They believe that these accountability measures, generally standardized tests, are slowly forcing schools to teach to the test in order to keep their funding. They believe that there is a wider experience that schools can offer than what can be measured on a standardized test. They also believe that the issue of failing schools comes to inequality in funding of schools, and more importantly the desperate inequality that exists in the US economic model. While the US is considerably richer than the rest of the world, the vast majority of that wealth is held within just a few people’s hands.

The problem is, if you belong to the second group anyway, is that the first message is gaining in strength. I believe that this is because the non-educator reformers have answered the why question with the parents of the US. They can point to a perceived failure in the system and then explain from the why, their how, and their what. They have a message which is compelling to many people but I believe that their solutions won’t work. The second group of people has suggestions for what, and for how, but their why is for some reason less compelling.

The solution the second group is offering is not going to work. They want to turn education system into a free market, but the market isn’t free if it is regulated, which is what the accountability measures they introduced with NCLB do. Maybe the premise that you can apply economic principles effectively to schools is flawed? 

Suppose we did apply a true free market approach to schools. We’d remove all regulations which would hamper schools and then fund schools based on market principles. Good quality schools would cost more, poor quality schools would cost less. Families would sue schools which were too unsafe, and schools would naturally tend toward offering choices that encouraged kids to attend. Some schools would look for corporate sponsorship to help them. McSchools anyone? Each family would have to decide for themselves what constituted a quality school and make decisions about where they would send their children.

The problem is that we would see legions of schools do things which look good, and are easy for parents to measure, but which are pedagogically unsound. Deciding on how effective a school is a difficult task, one most parents would find daunting if not impossible. They would have to rely on visiting schools and taking a look around to see what the school is doing. In any case, I think it would fail, and lots of kids would be harmed in the process.

The real question is, how can that first group of people change our approach and sell our (I think you know by now which group I support) vision of what schools can be? How can we find a reason why schools need to change which will resonate with parents? I think too often we focus on how we would like schools to change, and what steps we would take to make those changes, and that the important reason why those changes need to happen is lost. We are being beaten badly in the US court of public opinion, and we need to step up our game.

For those of you who wonder why I, as a Canadian educator, am so passionate about the education debate in the US, you just need to remember how often our politicians have looked south of our border for solutions. I’m not interested in any of the current US style of reforms taking root here in Canada.

Do these glasses end up with the same amount of each type of soda?

First watch this short video created by Dan Meyer so you understand the problem.

[WCYDWT] Coke v. Sprite from Dan Meyer on Vimeo.

I was having trouble wrapping my head around this problem. I saw people’s algebraic proofs, and I just felt there was something wrong with them. So I decided to construct a geomtric proof instead to make it more clear in my head.

Geometric proof

At step 1, both glasses have the same amount of liquid. At step 2, one glass has some liquid poured into the other glass. At step 3, we pour out the same amount of liquid from the right most glass, hence the area of the red rectangle is equal to the area of the vertical rectangle with the mixture of the two types of soda. Note that I’ve made sure to go the other direction in the diagram, so as to represent the fact that assuming the two liquids are mixed equally, essentially the soda I pour back is a mixture. In step 4, I note that area A + B is the same as B + C, because the two liquids are the same, and that the area of B is the same in both pictures, and so hence the area of A is the same as the area of C, which means that the amount of the first soda moved back and forth is the same.


Mathematics and Multimedia blog carnival

Here is the 8th Mathematics and Multimedia Blog Carnival for February (sorry it’s a few days late) with 8 interesting posts about mathematics.

Evolution of the symbol 8

Evolution of the symbol for 8

8 is an especially interesting number. It is the number of bits in a byte for example, and the number of sides on a chess board. It is the smallest composite Fibonacci number, and the only number (besides 1) in this sequence which is perfect cube. 8 = 23 and 8 in binary form is 1000.

This month we have a number of interesting articles, which I’m diving into sub-categories. You can check them out below.

Pure Math

John Cook presents an interesting relationship between the Twin prime conjecture and the Pentium division bug — The Endeavour posted at The Endeavour.

Guillermo P. Bautista Jr. presents a proof of The Infinitude of Pythagorean Triples « Mathematics and Multimedia which is posted at Mathematics and Multimedia.

Image shared by Gary Davis

Gary Ernest Davis talks about near misses in mathematics, or how computational errors from calculators can result in "disproving" famous theorems on his Republic of Mathematics blog.

History of Mathematics

Romeo Vitelli writes about The Mathematician In The Asylum posted at Providentia. "As it stand, Andre Bloch’s case represents a fascinating example of how even institutionalized psychiatric patients can continue having an influence on the world."

Mathematics Education

Earl Samuelson describes how he teachers an Introduction to Differential Calculus posted at Samuelson Mathxp.

I talk about how it doesn’t matter if students struggle understanding how algebra works, or by using a calculator, either way it’s still Mumbo Jumbo to them.

Maria Droujkova talks about how "[her] multiplicative, non-linear kid" is coping with learning about curvy and non-curvy functions and struggling with the vocabulary of linear vs non-linear. She makes a good point about how much of what we teach is a social construct, rather than a function of the mathematics itself.

Dan Meyer shows that you can get some deep, interesting and challenging mathematics just by asking questions about how well cheese melts in a microwave.


An argument against summative grading

Beth Still asks in a recent blog post

After being on Twitter for nearly 3 years I have learned to spot a bandwagon from a mile away. The latest bandwagon to come along has the words, “Let’s Abolish Grades!” written on the side of it. Maybe I am not as forward thinking or as innovative as I thought I was, but I don’t get this movement. Grades, whether they are letter grades, percentages, scales, or something else help students, parents, and teachers measure growth and progress and also indicate the level at which a student is performing (average, below average, above average). Students are admitted or denied access to certain programs, classes, and other things based on grades. Many times grades dictate scholarships and scholarships dictate where a student will attend college. This decision will have a lifelong impact on a person.

I responded

"I have no choice but to put zeros in their gradebook." Surely this isn’t true? A zero on an assignment is a slap in the face, and it certainly does nothing to encourage learning. You are not grading the student’s achievement, you are grading their behaviour. Those two areas need to be kept distinct from each other.

Here are my arguments against grading:

1. They are a shallow measure, they don’t tell the whole story. As a parent, I’d much rather have a complete picture of my son’s abilities rather than a brief summary.

2. They have a very high margin of error but are used for ranking students. Different teachers grade differently, use different assignments, but then students are all measured as if this wasn’t true. This is the equivalent of one scientist measuring in feet, and another in inches, and having them compare results without converting units.

3. They are so final! They end the learning rather than being an indicator of where further growth is. "Okay, well we finished that end of unit exam, here’s your grade. We’ll never think about that topic again."

4. They communicate the wrong message to students. Here is your F, clearly you know nothing about American History, or here is your A, now you know everything. Really? You can tell that a student knows nothing because of a letter they received?

5. Generally you know within a few DAYS of working with students what grades they will end up with at the end of the semester. To me, that says that the system must be rigged, because how could we possibly know what our students are likely to learn in advance of them learning? It’s like knowing the entire outcome of an experiment you’ve never done before.

6. They are used to rank students, schools, parents, communities. If you don’t think ranking is all that bad, remember that some educators careers, and student’s aspirations for the future are often dependent on a tiny variation between a "passing grade" and a failing one.

7. Grades are a cheap and easy substitute for parental involvement. "We absolve you of actually getting to know your child’s strengths and weaknesses within a subject area because we are going to give you the final summary of what they know in a single grade." Parents don’t have to feel guilty that they don’t know their children because they know their grades instead. This might be a little far-fetched, but think of the parents who act upon the final grades that their kids receive with punitive measures, rather than taking the time during the semester to be part of the learning process with their children.

I grade my students at my school, while recognizing that it is not a perfect system. It is a substitute for having sufficient time with parents and students to communicate the detail I think they deserve about their learning. We split the grade into "approaches to learning" and a summative score, which does help mitigate at least one of the issues Beth brings up in her post but I still find students searching for the final grade rather than being more curious about their learning progress.

I had a student recently who came to me after an exam, and told me she felt like she hadn’t done well. We sat down and went through her exam, and I gave her feedback on each question. We clarified what she understood, and where she had difficulty. It took about 30 minutes to go through the entire exam. I didn’t give her a mark, and say, "yep you did poorly now go away," I took the time to listen to her, find out what she felt like she understood, and give her the feedback she needs to improve her learning.

I recognize that I can do this because I have very small classes, and spending 30 minutes here or there with students to communicate feedback isn’t as big an issue as it would be with gigantic classes. To me, the biggest argument for a reduced class size is not that the students are "easier to manage" or that there is less grading, it is that you actually have the time to give students real feedback about their learning rather than a quick and dirty summary grade.

Cost of switching to Open License materials

I’m curious about the cost of textbooks in British Columbia, because I wondered, after doing some brief calculations in my head, how much textbooks cost in British Columbia, and how much an open source licensing system would cost by comparison. I need some help with my math, because I can’t understand why are still using the current system.

There are currently 649, 366 students listed as registered in British Columbia, according to the BC education ministry data website. If even half of those students have textbooks of some sort, and those textbooks cost an average of $25 per year for a typical 5 year replacement cycle, and if students take an average of 6 academic subjects then the total cost of textbooks in BC is about $50 million dollars. (I’m not able to look this information up easily, as most of the school districts in BC lump the cost of textbooks into their budgets for supplies). Let’s halve that number, in case some of my estimates are incorrect, which means that the cost of textbooks alone in BC is at least $25,000,000.

Of course this cost doesn’t include transporting the books, replacing lost, stolen, or damaged books, storing the books, and paying people to manage textbooks for schools or school districts.

What would an open source system cost? Imagine a system where the textbooks are written by authors, and then licensed under a creative commons license. The authors are paid a far wage for their work, but then not granted royalties once the work is complete. Please note that this is what I envision these "textbooks" looking like.

I would imagine that each course might have an author who is responsible for keeping the work up to date and maintained. If each of these authors earned $80,000 a year for their work, and we had an author in charge of each of 6 academic subjects, for about half of the students (so half of the current grades), then the total cost of the authors salaries would be $2,880,000. We’d probably want to have an chief editor of the project, so let’s add $120,000 for someone in charge of the project, to bring the salary total to $3,000,000. Further, I’m sure we would want to have a few consultants hired from time to time, expenses so that authors could attend professional development, type-setters to ensure the content looks clean, so perhaps the total budget for the project would be $5,000,000.

The authors would likely work in collaborative teams, so that although each author would be "in charge" of a specific textbook. Content changes regularly, so you would have to keep these authors on staff full time, as they would be constantly revising and upgrading their digital textbooks. The quality of the works would actually improve over the current model since any changes that needed to be made to the textbooks could be done so immediately, and then those changes pushed out to all of the digital copies of the textbooks students hold.

According to this analysis, you would save at least $20,000,000 a year using an open source model of publishing, with a conservative estimate of how much textbooks actually cost our province. I’m sure other educational districts could do similar analysis and see savings as well. Note that this savings does not take into account savings generated by not having to transport, store, maintain, upgrade, and replace textbooks.

Some other advantages of this system is that different provinces could collaborate and share units and modules of the text. We wouldn’t have to use just print resources, as I’ve argued before. Errors and omissions could be fixed on very short time-lines. The best explanation of a particular topic could be the one used, rather than relying on a single author (or small group of authors) to provide explanations. Textbooks could be shared with whomever wanted to use them. Parents and teachers could collaborate to provide translations of the textbooks.

A serious flaw with this argument is that many students in BC do not have devices capable of displaying digital textbooks and in some cases their existing devices that would work are actually banned in schools. This is an issue that needs to be resolved, however I think that $20,000,000 would go a long way toward providing students in need with some sort of electronic reader, especially if we leverage a lot of the devices students already have. (We remember that the replacement cycle on an ereader is about once every 3 years, hence we actually have about $60,000,000.)

To those who argue that this would further standardization of content across our province, you are right it would. However, currently the resources teacher use have restrictive licenses, while at least under a creative commons license educators, students, and parents could customize their textbook to suit their needs. There will always be a need for some form of a container to hold information, and for schools that container has traditionally been either the teacher or the textbook, in this system the container would more customizable and could adapt over time as our needs change.

There must be a flaw with this argument, something I’m missing. I was sure when I did these calculations I was going to end up with a different story, so please let me know what errors, omissions, and mistakes you see in my logic.