Improving Student AND Teacher Engagement

Today is report card writing day. I am one of those teachers who generally hates marking. I try and give mark-free feedback along the way as much as possible to keep students working on improving rather than obsessing about marks. But when it comes to report cards, a mark must be given, along with supporting evidence.

In my recent LTO positions, the "regular" teacher has left me more "traditional" units which overlap with their time in the class. I have also had some planning time LTO work where I rotate from class to class for 30 minute blocks of time, which has made more hands-on projects very challenging in terms of storage as well as set-up and take-down. This has left me with less freedom to do hands-on activities.

I really believe in the idea that we learn best by doing, by trying things out, by making mistakes and learning how to adjust and problem solve our way through a challenge.

This spring I have focused on making much of the learning hands-on. For science, the students created their own building companies. They created a name and logo for their companies. They had to apply their math to create and follow a budget for supplies and to draw out accurate building plans. They had to apply their understanding of internal and external forces. They had to determine and delegate smaller jobs to bring their project together, and so on. I incorporated building and safety permits, fines for noise and safety violations...you get the picture.

For language, they created and filmed book trailers or highly detailed book posters. For social studies, they took on roles throughout the study of first contact, and are working on building either a Fakebook profile or news article about a specific person or topic.

What I'm finding is that the more hands-on the activity, is, the more the students are engaged. They enjoy sharing their work and take a greater pride in sharing it than any more traditional paper-and-pencil tasks. This was not a surprise to me. What was a pleasant surprise is that the marking is becoming much more enjoyable to me as well.

My tea is nearly ready as I sit back and watch a second batch of book trailers. Netflix has nothing on my students in 5A!

Working Backwards

Looking through many resources in preparation for teaching math in the school system, there seems to be a very common pattern that is rarely broken: introduce algorithm, apply it to increasingly difficult pre-determined problems, review, then tack on a "real life" or "word" problem to add application as almost an afterthought. Some resources even skip this last step, and few indeed involve proofs, aside from a couple that show how to derive the quadratic equation.

In mathematics, we have a tendency to ask students to accept algorithms without question or debate. We essentially eliminate critical thinking from our teaching.

This is not the way teachers are trained in my province, yet many resources that are used in our classrooms still follow this sequence, and many teachers drift toward this in their practice. The emphasis remains on the lower levels of Bloom's Taxonomy at the expense of activities that promote higher-order thinking. In my review of the literature, it appears that teachers are most likely to work in this direction for two reasons: this is the way they were taught, and their comfort level with the curriculum is low.

When I say their comfort level is low, I do not mean that they do not necessarily hold a deep conceptual understanding of the topic, but that for various reasons (most often relating to allotted classroom time), they feel the need to get the basics covered as quickly as possible, and for many, teaching algorithms is how they view "the basics" when it comes to math.

But what if we were to reverse this direction, and start with the applied problem?

Critics say that this leaves students high and dry, with the need to reinvent conceptual knowledge that took mathematical superstars many years to develop. They say it leads to confusion when the approach they might try is not the most efficient method.

However, no one is saying that we withhold the algorithms from the students, only that we let them think about the problems that lead to them in order to foster a sense of pattern and deeper conceptual understanding of the processes involved in applying mathematical thinking.

All the memorized algorithms in the world are useless if students never learn when or how to use them outside of math class or standardized testing.

Sure, it takes a little more time for students to think through the "why" of a problem, but feeding them algorithms to memorize and apply does students a disservice. Computers can work through algorithms, and they do it faster and more accurately than people. What we need are people who can reason mathematically, and this requires that we provide a space for applied problem solving and reflection.

It is my gut feeling based on what I've seen with the students I've worked with that students who develop applied problem solving skills aka mathematical reasoning skills, begin to make deeper connections quicker with later topics. In this way, the time invested at the outset may offset the time needed to cover later related topics.

For teachers to abandon the chalk-and-talk and promote these skills will take a leap of faith. It is much more comfortable to stay with the known, particularly when there is a perceived crunch in terms of curricular content demands and the allotted classroom time to cover it. Students may resist since they are used to being given the entire topic at the outset. People tend to resist change.

How many times have we heard the question from our students, "When will we ever use this?". Students, particularly those for whom math does not come easily, need to understand this in order to invest their time and effort accordingly. Resources like this one: 101 uses for a quadratic equation and this one: "Why study math?" can be good places to start. Starting with a relevant real-life problem is also an effective way to connect theory with application.

I issue the following challenge to all teachers who read this blog: choose one topic this year to present this way and see how it goes. Start with a real-life problem, challenge students either individually or in groups to devise a way to tackle it, and share results using Bansho or another similar method in which the different approaches can be grouped in a meaningful way. Discuss which ones work and which don't and why. Finish with a review of those ways that work best. Follow up with some practice problems.

Did you or your students resist? What challenges did you face? Did different students participate than usual for your class? How might you use this to best encourage mathematical reasoning in your students?

File Folder Games for Middle Grade Students

Maybe it's because my initial teacher training focused on the primary grades, but when I decided it was time to start making supplies for my future classroom, file folder games quickly came to mind.

Doing a quick Google search showed me that few, if any, teachers are using this concept with older students. I'm not sure why this might be, but I have decided I will not let it stop me in my quest for useful and independent activities students can work with once their classroom work is complete.

Why would I use these with older students?

1. Portability It is likely that I will work as an occasional teacher for a while, so portability is mandatory. Even within a single school, there is a chance I would need to move from classroom to classroom depending on the school's schedule, so portability is always a desired feature.
2. Enrichment Opportunities No student wants to be faced with "more of the same" or be forced to help other students when their work is complete. Providing recreational math games in one way to help students extend concepts without extra drill and encourages them to think strategically.
3. Thriftiness The cost of purchasing plastic commercial versions of some of these games would be prohibitive. The bulk of the games would also make them cumbersome to carry and difficult to store. I can make similar versions of these that cost less, take up less space, and are laminated to improve durability. A missing piece can be easily reprinted.
4. Versatility Laminated surfaces lend themselves well to dry-erase markers (or even crayons that can be wiped off in a pinch). This means games can be adapted to suit current needs, and it also means that popular paper-and-pencil games can be played with less paper waste involved.
5. Novelty If I can't find them online, chances are good that most middle grade kids aren't used to seeing file folder games as part of their math instruction.
6. Play Value Introducing new concepts through play can help students develop a deeper understanding of the underlying concepts. Playing a code-breaking game can help introduce the concept of combinations and permutations, for example. Probability, geometry, co-ordinates etc. can also be introduced through game play. While the folders lend themselves well to after-work activities, they can also be used to introduce concepts to the entire group. When the focus moves away from computation and "right answers only" into the underlying concepts and strategies, many students feel less threatened with the introduction of new concepts. As we would not forbid a toddler to use a word he or she could not yet write or spell, we can encourage students to develop meaning and concept through games and exploration before demanding computational accuracy.

The games I will be making include many from my math pages here: http://llemonade.com/math and here: http://llemonade.com/math2 These include classics such as Dots, Hex, Black, Birdcage and several others. What is wonderful about these kinds of games is that most of them are traditional and quite old, and as such, remain in the public domain.
If you wish to use any of the boards I have drawn specifically for my site, you may, with the caveat that these are for personal use, which includes homeschooling for a single family, use for a single classroom, or recreational use at home. Many hours of work go into the development of the resources I share. If you wish to make these and sell them or otherwise distribute them, you will need to contact me with the details so we can come to an arrangement.
Once I have completed the math games, I will likely print out some Madlibs from my print page as well, primarily for ESL students, but also available to all students upon completion of the main classroom activities.

As I have completed the basic games and ensured that the layout works, I will share those printable boards and rules on the print page as well.

This is the process I use:

1. Determine the game to be used and divide it into three main sections: the rules, the board, and any playing pieces.
2. Create separate files for each section and print these out. Since the games are aimed older, they are less clip-art oriented and quite minimalist, but clip art and other graphic features can be added as desired.
3. Create a cover piece that included the title of the game and the number of players required.
4. Print all of these out on regular printer paper.
   
5. Trim the printouts as needed.
6. Paste the board to the inside of the folder. Larger boards must not bridge the folded area as they may make the folder too bulky to fold. Paste the cover on the front and the rules either on the inside left of the folder, or on the back for larger boards.Laminate the folder and playing pieces separately.
7. To make a pocket that is both laminated but which you can open up, see this excellent blog post I found that has clear instructions complete with pictures http://lifeasaconvert.blogspot.ca/2011/09/how-to-attach-pockets-to-file-folder.html
8. You can also paste the pocket right onto the folder before laminating if you do not need to be able to close a flap. This eliminates the need to use velcro to attach it later. If you want the best of both worlds--a pocket that has a flap you can close and is sealed onto the board with the lamination rather than velcro, try lining up the pocket at the edge of the folder so the flap extends beyond the edge. It can then be folded at the edge of the folder. It may be a little bulky, but the pocket will not be easily lost.

Enjoy!

Educational Ideals--An Afterword

Seth Godin sums up many of the issues I have addressed on education in recent posts. Since he is more eloquent than I, I have included his TedTalk here.

Of course, the system he addresses is that of the United States, but here in Canada, and also in other parts of the world, there are many features that are similar and need to be addressed.

One thing he speaks about is the "Flipped Classroom". The backlash against this concept is astounding to me, but I think that there are some other things going on here that have contributed. 

For one thing, it assumes internet access. While most people have this, there are still many who do not, and this can put those students at a further disadvantage. 

I have seen so-called "flipped classrooms" where the teacher watches the students all watch the same lecture. For this, I'm not even sure where to start! Certainly this is a huge waste of time and resources. The lectures and resources are supposed to happen away from the teacher; the discussion and application are what the teacher and class are there for during the classroom time.

I also wonder how this can be used in classrooms that are deemed "inclusive" and in which the abilities and needs of the students are extremely diverse. I would argue that both interest and ability groupings may be the most effective way to encourage all students to reach their potential. 

People have criticized Sal Khan for not being a complete resource unto himself. That is as ridiculous as saying that a research paper with only a single source is complete. Life doesn't work that way. Students need to learn to consult varied resources and to consider biases and limitations within those sources as part of learning critical thinking. Khan Academy, TedTalks, MIT Courseware, PI Lectures, and a multitude of other online lectures are now available, as are websites, internet chats, email, and yes, even textbooks. There is no need for a teacher to present this at a single speed to a classroom of students. Where the value of a teacher lies is in generating discussion, and encouraging students to delve deeply and ask questions, to think of things in different ways, make connections and apply these concepts in new ways. Round-robin reading of a textbook is no more than a way to fill in time. Wasting the time of our students is quite possibly the most disrespectful thing we can do as teachers.

I do disagree though that there is no place for textbooks in exciting students to learn. I do think though that they should be treated as reference materials rather than the main or sole source of information, just as we might consult a dictionary on occasion but are unlikely to sit down and read it cover-to-cover.

What are your thoughts on flipped classrooms, and education in general?