The Reflective Educator

Education ∪ Math ∪ Technology

Year: 2011 (page 7 of 28)

September 4, 2011 / 6 Comments

New York Times article misses the point

Matt Richtel, of the New York Times, has recently written a piece on the use of technology in schools which should be read carefully. He writes:

Since 2005, scores in reading and math have stagnated in Kyrene [emphasis mine], even as statewide scores have risen.

To be sure, test scores can go up or down for many reasons. But to many education experts, something is not adding up — here and across the country. In a nutshell: schools are spending billions on technology, even as they cut budgets and lay off teachers, with little proof that this approach is improving basic learning.

This conundrum calls into question one of the most significant contemporary educational movements. Advocates for giving schools a major technological upgrade — which include powerful educators, Silicon Valley titans and White House appointees — say digital devices let students learn at their own pace, teach skills needed in a modern economy and hold the attention of a generation weaned on gadgets.

He has assumed that the purpose of education is to improve test scores, or at the very least that these are a good measure of learning. He has also generalized about the use of technology in classrooms across the US from two examples; a single school district, and the state of Maine. He is right that many schools are spending money unwisely on unproven technologies, and have not put into place practices to either support these technologies, or examine their effectiveness.

Aviva Dunsiger has written a response to this article based on the results of a direct reading assessment (DRA) she’s done during the course of the year. She doesn’t attribute the phenomenal gains on the DRAs to the use of technology in her classroom, she attributes it to the change in her teaching practices that resulted from the technology being available in her classroom.

This is my reason for promoting the use of technologies in schools. The introduction of computers in the classroom has the ability to be a disruptive force, and transform the pedagogy that is used in the classroom. This doesn’t mean that it will transform pedagogy, it just has the possibility to do so. In 50 years of attempts to change the classroom, nothing has come as close as this current driving force from technology.

In 1993, Seymour Papert wrote,

"Video games teach children what computers are beginning to teach adults–that some forms of learning are fast-paced, immensely compelling, and rewarding. The fact that they are enormously demanding of one’s time and require new ways of thinking remains a small price to pay (and is perhaps even an advantage) to be vaulted into the future. Not surprisingly, by comparison School strikes many young people as slow, boring, and frankly out of touch."

While it is possible to teach in ways which are compelling and rewarding, many schools do not do so. Technology in the classroom can be a lever through which we effect real change in our schools in a positive and fundamental way.

September 4, 2011 / 2 Comments

Fixing Math Education

I’m in the middle of researching different proposed solutions to "fix math education." I’ve started classifying these proposed solutions and am hoping I can get some help to look for more possible solutions, and to flesh out the arguments supporting each of these various solutions. I’ve also added some resources into this document (like videos & essays about math education) and would love it if people could add more videos in particular as well as pivotal essays discussing math education.

Access & edit this document here.

I’ve embedded the document below if you’d like to read it without editing it. Please feel free to add comments to the document if you don’t feel comfortable editing it.

September 3, 2011 / 12 Comments

Questions about the flipped model of instruction

I’ve been reading a lot about the flipped model of classroom instruction, where students watch instructional videos for homework, and then do the practice and problem solving during class time. Here’s a video of the process being explained by Aaron Sams.

 

Some of the questions I have are pretty much the same as the ones posted as responses to the YouTube video so I’ll just quote them:

I’m curious as to what you do with kids who don’t have the internet or a computer at home? I see someone else asked this question below, but I don’t see where that was answered. This seems to be just another way to divide classroom success socioeconomically. ~ Rubyfreckles78 

What if you don’t believe in homework? What if you believe a child’s time outside of school should be their own, to explore the other adventures life has to offer outside the formal academic arena? ~ katiramom 

"What to learn, how to learn it, when to learn it and how to prove to me that they learned it". I can see that the times of learning has changed but is it not still teacher-cetred in this respect? Yes, a different modality – online and video (great!) but what underlying structural changes in terms of power and student-centredness? "We’ve changed the place in which content is delivered". In what ways are the pupils negotiating content? ~ audhilly

This is great, Aaron. Unfortunately, some school districts–like that one I work in–do not allow their teachers to access Youtube. ~ l2spanishteacher

It seems to me that there is no good answer to the first question. Students without parents at home, who are homeless, or who do not have access to technology at home to view these videos are out of luck. They’ll have to stay at school to watch the videos in the library.

As for the question about homework, this to me is the biggest question I have about the flipped model. It assumes that the time kids spend outside of the classroom should be taken up watching videos. In essence, the flipped classroom model assumes that the instructional time schools are given is insufficient for kids to learn the material. Perhaps we there is simply too much content for kids to learn effectively?

The third question is mostly about pedagogy. Should kids learn in a teacher-centred way, or a student-centred way? While our curriculum is bloated and filled with content, it seems impossible to switch to a more constructivist model, particularly in the upper grades. Constructivist teaching methods take more time than more traditional methods of teaching (but hopefully lead to deeper understanding). 

The fourth question is similar to the first question as that both of them are about access. Clearly the solution here is for the school to self-host the videos, but if this becomes a common instructional strategy at your school, the costs incurred to host what could be thousands of videos is enormous. Now we have an issue that the schools with the money to afford the hosting (or at least the policies in place to allow YouTube and other video hosting sites) are a further advantage to the poorer schools.
 

Some more questions I have are:

  • What does this approach look like for someone who is a novice to teaching?

    One of the valuable pieces of feedback a novice teacher gets about their instruction is the questions students ask during class. Students will often share misconceptions they have about whatever is being taught, which helps improve the teacher’s delivery for the next time. While I think an emphasis on lecture based instruction is not the best possible pedagogy, it certainly is an easy place for novice teachers to start during their career. Flipping the classroom could reduce the feedback the teachers get on their instruction, but see my next question.
     

  • How do students ask questions?

    Students need feedback during learning as well. One of the points of practice problems, and of problem based instruction, is to maximize the number of opportunities for feedback during learning for students. Lecture based instruction typically fails in this regard, and so many instructors have switched over to discussion based instruction. The flipped classroom model, without a way for students to actively ask questions, moves instruction back to a purely lecture based format. One way to counteract this a bit would be to provide space for students to ask (& answer) questions underneath the video lecture as comments, but then the job of the teacher will be to moderate and join into these discussions. While students can obviously record the questions they have (which is a useful learning strategy), this requires organizational skills and self-management skills not every student possesses.
     

  • How much time does it take for teachers to make these instructional resources?

    Preparing for classes and assessing students are the two tasks, other than administrative paperwork, that take the most time for teachers during the course of their day. Preparing high quality instructional videos has certainly become much easier for teachers to do, but it is also time-consuming. Sal Khan might be able to create 8 videos a day, but teachers do not have their entire day available to devote to making videos, and would like to produce videos which include images and animations to clarify some concepts. We could rely on the videos from sources like the Khan Academy rather than making our own videos, but we’d need to search for and preview all of the resources we use, which in itself is time-consuming. There is also the additional time spent during our evenings responding to questions students might have about the videos.
     

  • Will class time be used more productively?

    Aaron’s video above shows some great examples of what I think should be happening in more science classes. The students look like they are getting more chances to experiment, and more chances to interact with and actually do science. Is this what happens in every flipped classroom? If students really understand the concepts being taught by the end of a unit, how can we tell if it was the instructional video, or the time spent actively experimenting that made the biggest impact on their learning? One comment I had from a student was that although his teacher assigned videos for homework, he rarely watched them, but made sure to actively participate and learn during class time. He loved the flipped model because "it meant [he] had less homework."
     

Although I have these questions, there are some things which I really like about the flipped model of instruction.

  • It forces teachers to really think about their instructional strategies and the potential questions students might have.

    You can’t create these videos without putting some serious thought about what you will be teaching for that lesson. This particular type of teaching is much more difficult than turning to page 27 in the textbook and selecting some questions for students to do.
     

  • Students can potentially access a variety of different explanations for different concepts from teachers all over the world.

    Not every student has access to a specialist in their subject area. In British Columbia, for example, there are many teachers teaching math outside of their specialty. I can remember tutoring math when I was in grade 11 in the PE teacher’s classroom (who was not a math specialist, or trained to teach math) and frequently helping the teacher understand the math he was "teaching".
     

  • It provides more class time for more student centred instructional strategies.

    This is the best reason to implement the flipped classroom model since many teachers aren’t ready to give up on teacher led instruction. Students need more time processing the concepts to which they are being exposed. If they do this at home, as is unfortunately too typical in many classrooms, they struggle. In the flipped classroom model, that struggle can happen with their peers and an expert facilitator.
     
  • Students can now more easily opt out of rote memorization.

    Richard Feynmann, one of the best physics lecturers of all time, investigated Brazilian science education, which was heavily dominated by memorization, and discovered that almost no one from this system actually understood science. Since students do not learn well from memorizing information, one can conclude that lecturing is not sufficient to produce students who understand concepts at a deep level.

Does anyone have any answers to these questions?

 

September 1, 2011 / 0 Comments

Improve math education with rote learning?

Priyamvada Natarajan has written an article on the Huffingtonpost about how she thinks we should improve math education. She says:

We are failing to teach our children the fundamentals of mathematics and quantitative reasoning skills. These skills form the foundation upon which future technical education is based. Children do not attain adequate proficiency, develop math phobia and as a result we lose a vast talent pool of potential engineers and scientists. Most of the high-paying jobs of the future will require mathematical fluency — a skill that most American students leaving school do not come close to possessing.

…

Finally, it’s time to return to old-fashioned rote learning. My work now involves complicated and abstract math, but I started where everyone can: with the multiplication tables. Here are two truths: 7 x 5 = 35 and developing dexterity with mental arithmetic leads to comfort with quantitative reasoning.

I responded:

As an alternative to this article, see: http://www.edutopia.org/blog/mathematics-real-world-curriculum-david-wees

The issue, in my opinion, is not that students are not learning computations, it’s that they are rarely learning these computations in useful contexts. The "fake" textbook word problems that are presented to students are an attempt to develop some sense of context for students, but most of these fail to address the cultural and socio-economic differences in students.

Keith Devlin talks about this issue in his book, "The Math Instinct", which I consider to be part of the required reading for all who are interested in math education reform. Further, I would add "A Mathematician’s Lament" by Paul Lockhart and " The Four Pillars Upon Which the Failure of Math Education Rest" by Matthew A. Brenner (see http://www.k12math.org/doclib/4pillars.pdf).

Another useful video to watch  (created by Gord Hamilton of http://www.mathpickle.com) has another perspective on this issue. Watch it here: http://www.youtube.com/watch?v=3sN3dEVeMb8

As for the utility of the Khan Academy videos, see Derek Muller’s video where he demolishes the notion that kids learn effectively from standard video lectures: http://www.youtube.com/watch?v=eVtCO84MDj8

The issue in math education is complicated. You can’t just say, "increase rote memorization and everything will be better" because the world has changed since that was necessary. We don’t live in a world where memorizing everything (note: memorizing some things is still useful) is necessary. We don’t need to carry rote memorization in our heads as much, so long as we understand how and why we can access the information.

 

Another issue (which I did not include because I ran out of words) is that people, who are well-meaning but not knowledgeable on the issue of math education, keep suggesting rote learning as an alternative to our current system. "More of the same" is not a solution to the problem. I’m fine with people presenting alternatives to our current system, but if you are going to post in a high profile location, I strongly recommend you do your research first…

September 1, 2011 / 3 Comments

Standardization is impossible

Stop light
(Image credit: photoburst)

 

Stop lights are a rule. They are a standard system used worldwide as a solution to the problem of people getting into accidents at intersections.

However, what most people don’t know (unless you have travelled a lot, or lived abroad) is that different cultures treat stop lights differently, particularly for pedestrians. In New York City, the red light means "walk across unless someone is driving through right now" on a cross town street, and "don’t walk" on a uptown/downtown street. In Vancouver, the red light means "be careful crossing the street" if it is a quiet street, and "don’t cross" (unless you are a rebel) for a busy street. In London, a red light means "stay the hell away from the road" because cars will run you down if you try and cross, but a crosswalk means, "expect traffic to slam on their brakes to let you cross". In Bangkok, you don’t cross at intersections, you use the overhead walkways. In Hamburg, the red light means, do not cross under any circumstances, even if you can’t see traffic in either direction for miles. In Rio de Janeiro, at night time, the red light means, honk and drive on through, as no one wants to stop in case they are carjacked (anyone who walks around Rio at night time is crazy).

The point is, this seemingly universal symbol still has a local meaning, even though effort has been made to adopt the same system all over the world. Rules are culturally situated.

Our society’s push to standardize education needs to recognize that even in a standardized system, there will be local variance. Schools, just like municipalities adopting traffic lights, need to work the external system into their local framework, and the expectation that every school should come up with the same solution is flawed. In fact, some schools may have very different approaches to applying the standardized framework to their local community.

Some municipalities have nearly abandoned the traffic light as a form of managing traffic at intersections. 

Round about

 

What is the parallel to the round-about in education? Is this completely different than standardization? Should our system have the flexibility to allow more schools to choose different solutions to education?

August 29, 2011 / 4 Comments

The PALS program – hope there is more to it than this

 

This is a video of a teacher sharing an example of the PALS math curriculum in action. The pedagogy in this video though frustrates me though, and although the idea of Peer Assisted Learning Strategies (PALS) seems good, I don’t think the approach this teacher took is very good.

  • She’s using rewards to encourage kids to work with each other. Alfie Kohn does a good job of explaining why this is problematic. "The smiley faces help you remember to mark points." She also spends nearly a minute describing to the kids how to do the task. My experience with kids this young (or any age really) is that they don’t have the attention span to remember something as complex and essentially arbitrary as the instructions necessary to this task "the teacher’s way."
     
  • The students actually have very little interaction in this video with the numbers themselves. The symbols aren’t the numbers. In fact, I think they are an unnecessary layer of abstraction on the concept of number at this young age. Kids need representations of numbers that are more concrete, and once they have a concrete understanding of the concept, then you can move into the abstraction. The entire objective of this lesson seems to be to connect one abstraction (the verbalization of the numbers) with another abstraction (the symbols that represent the numbers).

    If you want kids to learn about these two abstract representations, then you should pair them with a concrete representation with which the kids are more familiar. For example, the symbols should be paired with objects (ie 8 blocks paired with the symbol for 8). You should also teach the two abstractions independently of each other, if at all possible, at least when introducing them.
     

  • It’s clear from the way the kids are reciting facts after this teacher asks questions that they do a lot of this. Reciting something verbatim doesn’t mean you understand what you are doing. In this entire clip, the teacher doesn’t give a single piece of feedback to the students about their learning. Learning is a process through which you incorporate feedback from the world into your existing schema of the world. The only feedback the kids get is the voices of the other children saying the same thing as them, which is minimal at best.
     
  • Not a single kid gets to ask a question, like "why do the numbers look like that?" What would be the harm in the kids spending some time creating their own number system, and then matching it to our existing one?
     
  • It seems like the interaction between the kids is forced. I’m sure there must be more natural ways of discussing the numbers and providing feedback to each other on understanding of the numerals than this contrived activity. 
     

In fairness, I cannot tell from this video anything more than this particular 5 minute segment of this one teacher’s class could use improvement. There does seem to be some evidence that this is a typical 5 minute period, at least at the beginning of class, but it could be that the rest of her class is wonderful. I do think that I wouldn’t share this particular 5 minute clip as example of good pedagogy.

August 27, 2011 / 1 Comment

Numeracy for preschoolers

Count 10 Read 10Bon Crowder has started an initiative to embed numeracy in the early lives of children via their parents, which she calls Count 10, Read 10. The basic idea is to split up the 20 minute of reading for parents into 10 minutes of numeracy and 10 minutes of literacy every day. 

Most parents aren’t reading to their kids daily (only about 48% in the US do) which is hurting their abiliy to learn how to read when they get to school. Unfortunately, an even smaller percentage of parents engage in daily numeracy building activies. If you think not being read to impacts your ability to be successful in school, imagine what happens if you can’t count.

Only 45% of adult Canadians are numerate, "demonstrat[ing] skills and knowledge associated with the ability to function well in Canadian society." By comparison, 52% of adult Canadians demonstrate the minimum levels of literacy required for a person to function well in today’s society. Neither of these numbers is very impressive, but clearly our society is doing a slightly better job preparing people to be literate.

The importance of an early start in numeracy has been well established. While the relationship between the ability to do math and being numerate is not completely clear, the relationship between early numeracy and later numeracy should be. Parents can have a strong impact on the numeracy of their children, and should engage in early numeracy building activities.

One issue, besides of course having time to do these activities with their children, is that many parents don’t know many strategies for building numeracy. Just as educators provide strategies for parents to use to develop early literacy skills, we should do the same to help parents with early numeracy strategies for children.

As a parent with a strong sense of numeracy, and an educator, I have some activities I’ve done with my now 4 year son which you are welcome to share with parents.

My son, wife, and I count everything. We count stairs as we climb them, we count plates as put them out on the table, we count down from 10 when we pretend to blast off in our rockets, and up to 10 when we play hide and seek. We count by twos, we count by fives, and we count by tens. We talk about the relative size of numbers, and use language like less than, more than, and other mathematical comparison language.

Playing chess

We play dice games, like Backgammon or Parcheesi and recently even more advanced dice rolling games like Titan. My son counts up the two dice by himself to see how far he gets to move, and then counts to move his pieces. We play Chess together, and my son’s favourite part of this game is making up rules for how the pieces can move. We play card games together, like Go Fish and War which not only let my son see both the numerals, and a representation of the number on the cards themselves, but also look for comparisons between numbers.

My son bakes and cooks in the kitchen with both of us and is learning about ratios in food, and fractions in baking. We split cookies into halves when sharing, and cut sandwiches into quarters. We talk about food and how old my son is in terms of fractions. He knows he was once four and a half, then four and three quarters, and now he is four and eleven twelfths. While he doesn’t know what eleven twelfths means yet (although he does understand halves and quarters), the fact he has heard about fractions being used in context allows him to start developing some meaning for them.

We build patterns together. We’ll stack blocks into stair cases. We’ll talk about the shapes of blocks using their names (like pentagon) and together we will explore the similarities and differences between his shapes. We make circles out of his train tracks. One of his favourite toys is his magnetic blocks, which he builds into many different types of shapes.

We also play number games like "How can I get to __?" How this game works is that given a number, you try and figure out different ways to get that number by adding smaller numbers together. For example, 1 + 1 + 1 + 4 = 7. 1 + 2 + 1 + 1 + 2 = 7, and so on. I even recently taught my son how to play Nim, which is a great game for teaching about looking ahead.

The point is, my son is immersed in a world of numbers and his ability to see the world through numbers later in life is greatly increased.

August 24, 2011 / 3 Comments

The difference between a question and a quiz

A question is a statement which is asking for the answer to something for which the teacher honestly does not know the answer. A quiz is a statement which assumes that the teacher knows something about the statement, and is checking to see what the person being asked knows. As John Holt suggests, a quiz demonstrates a fundamental distrust between the teacher and their student.

A question leads children to think about possible answers, and a quiz leads children to find either a way to avoid the question, or feel uncomfortable because they aren’t sure for what answer the teacher is looking.

Make sure you ask questions when you want kids to think. If you must quiz students, make sure that they are clear about the purpose of the quiz, and do it in such a way that "I don’t know" is an acceptable answer.

Here are some quizzing techniques to avoid if at all possible:

  • Asking and answering. There’s not much point in asking something if you are just going to turn around and answer it right away.
     
  • Asking that which relies on kids being able to read your mind. This turns kids into guessers.
     
  • Asking that which being able to respond requires that you had to be paying attention moments ago. Turning your quizzes into opportunities to catch kids daydreaming makes kids less likely to want to answer any of them. Everyone loses focus occasionally, find another way to deal with the issue.
     
  • Asking that which is entirely obvious. If you know it is obvious, and the kids know that the answer is obvious, asking about it is just going to make the kids think that you think they are stupid.
     
  • Making rhetorical statements. These aren’t really questions or quizzes but rather a way of presenting information in a confusing way. Your students for whom English is a second language don’t like rhetorical "questions" because they are confusing and useless.

What are some other quizzing techniques we should avoid? (This is a question, since I don’t know the answer, and am actually curious about your thoughts.)

August 22, 2011 / 4 Comments

A problem with the problem-solving process

Problem solving in life is rarely a linear process. In fact, when I think about how I solve problems, I find myself using something like the following process.

Problem solving process

 

Creative Commons Licence

 

I try out different strategies for solving the problem, but I don’t start with the same strategy all the time, nor do I follow the same steps. Often I’ll skip some of the strategies above, and I very rarely spend the same amount of time working on each step.

The walk-away step I discovered after I finished school. I realized that I would often solve problems at unexpected times, either when my mind was focused in other areas, or unfocused completely. This is not a uncommon occurence, I have read about and talked to many people who note that the solution to problems came to them in similar circumstances.

How do we teach students about the importance of walking away from a perplexing problem sometimes? Can we trust them to walk away but come back to the problem? How do we show them that problem solving is not a linear process? How can we impart the difference between collaborating with someone else on the solution to a problem, and relying on others to solve problems for us?

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