Education ∪ Math ∪ Technology

Day: January 20, 2010 (page 1 of 1)

What would you tell a new teacher?

I had the opportunity to have a new teacher hang out in one of my classes today.  We had about a 20 minute discussion afterward where she asked some questions and I got to share a couple of resources.  She is being trained to teach Math and Science so we have a lot of overlap in our specialties.

First we talked about instructional strategies.  I mentioned that I don’t assign exercises from the textbook anymore, I haven’t all year.  I read brain based research which talked about how important immediate feedback (related meta-study) is in the learning process and realized that there was no effective way to have an exercise from the textbook tell my student what they are doing wrong, it just doesn’t work.  If I give any repetitive exercises at all, they are online quizzes hosted at either (if I want to create the quiz myself) or (if I want the students to have more open ended questions and more feedback).

I also mentioned that I focus on including real life examples of everything I teach.  In other words, every unit has at least one (usually many) examples of ways this math is used, or could be used.  I’ve got a bunch of examples up here, more to follow later.  The idea is obvious to me, connect what you are doing in class to what the students will be doing outside of your class, or at least to things they are interested in outside of class.

I talked about my strategy during my first years as a teacher.  My first year I focussed on surviving, I started my career in inner city Brooklyn so this was a necessary survival strategy.  My second year I started experimenting.  Every week I used a different instructional strategy.  In my third year I tried a new thing two or three times a week.  Every year I’ve been teaching I’ve created all of my lesson plans from scratch every day for every lesson.  It has forced me to reflect on my teaching and I think it has helped me to keep improving my practice.

She asked for some website resources and I gave her the ones I mentioned above, and she said that it was SO difficult to find resources in today’s age because there are so many resources to choose from.  The ranking algorithm of Google is good, but not perfect and doesn’t always help find the best resource for you.  So I pointed out Twitter.

I said that Twitter is like having however many people who are your followers acting to do some of your research for you.  Ask question, get an answer.  See a question, give an answer.  Follow 1000 people who Tweet regularly, multiply your productivity 1000x in terms of searching for resources and information, assuming you follow the right people.

What would you share with a new teacher?

More advice from Twitter PLN:

penphoe @davidwees re: new teachers, "5% lesson content, 95% dealing with people"

sharon_elin @davidwees I’d tell new tchr "Put bureacracy aside; it’s all about you & the kids." Relationship 1st, w/you as curiosity coach (not peer).

Philip_Cummings @davidwees Dear New Teacher – Develop a PLN & pick a really good mentor.

acmcdonaldgp RT @davidwees: I would tell a new teacher: Build GREAT, appropriate relationships and never take away hope!

rrodgers @davidwees Be adaptable and process-focused, and he end results will take care of themselves.

amichetti @davidwees I would say that the most important thing to remember is to be flexible!

misterlamb @davidwees "Teaching is your job, it’s not your life." Advice from my co-op from student teaching. Make time for yourself.

TSherwood @davidwees That it’s OK to cry. There will be more smiles than tears. 




Idea for alternate school structure – School without a daily bell schedule

So I was just walking up the steps and had an idea.  What would a school without a restrictive bell schedule look like?  I was wondering about this because I remember so many times this year having students working along in a great groove on one of my projects, and then suddenly time is up and the students all have to move to another room!  This is very frustrating, especially if another 10 minutes means they could finish their train of thought.

So what would it take to make this work?

First, teachers would need to have daily small group planning time built into their schedules, probably every morning.  They would need to plan how the schedule was going to unfold that day and to review on a daily basis the progress of the students.  Technology could be used to help keep track of where students are at so that teachers don’t have to push around gigantic piles of paper. Update: Or as John Holt suggests, we could trust students more and give at least some of them more ownership over this process.

Next, the curriculum would have to be broken down, not into subject areas (except for review possibly for external certification) but by project.  Each project would have to have the traditional subjects integrated into it, with percentages (and specific skills or content areas) for how much the project counts towards each subject.  Students would have individualized education plans because the teachers would have the time to construct plans for each student. Update: Again, this would be easier if at least some of the students, or all of them at some stage, had more control over what they were learning, and when.

Assessment would be standards based assessment.  Partially this is because it is a bit easier to assess a bunch of students who may be at difference places in your curriculum using standards, and partially because I believe that standards based assessment works better than norm referenced assessment.  Finally another argument for standards based assessment is that students should move through standards, rather than through grades.

Another thing that might be possible to remove in such a school is the barriers that we construct between students of different ages.  Clubs quite often have students working together with very different skill levels and ages, and quite a large number of school clubs work quite well.  So it’s not impossible for students of even very different ages to work efficiently together.  As well, it might be that students of different ages are working on very similar projects or even the same project (being assessed differently because the standards might be different for each student).  So what I envision is a school without grade levels and maybe with a very different layout or structure.

Perhaps this school is architecturally different as well.  Students would need some private space to work (maybe in multilevel groups so that older students have the responsibility to check on the younger student’s progress and model appropriate behaviour?), many small group sized rooms, and some wide open places as well.  The small work spaces could be offshoots of the general meeting areas which are in turn offshoots of a larger wide open space.

Every student should have to do some physical activity each day.  Physical education is SO important for children, their bodies are built to move.  It would be one of the core classes in a school like this instead of an aside that is government mandated.

What else do you think this school needs?  Are there any schools which are actually like this?

Update: Of course, I’ve made some pretty broad assumptions in the original version of this piece – one of which is that every student should learn exactly the same thing. While I do believe that a liberal education (in which one learns about a wide variety of things) is important, there are many, many different ways to achieve that outcome.

Authentic learning experiences

This year I have really tried to step up the process of bringing the real world into my mathematics class.  A major focus has been on using technology appropriately as a tool to help solve real life problems.

Here are some examples:


Distance formula:  Finding an optimal (or near optimal) solution to the Traveling Salesman problem for a small number of cities.  

Basically here the students were given the assignment of choosing 6 or 7 cities fairly near each other on a Google map and finding the x and y coordinates of each city, then using the distance formula to determine the distances between the cities.  Once they had this information, they were to try and figure out a shortest path, or at least something very close to the shortest path, and then justify their solution.


Linear graphs & Piecewise functions:  Compare 4 or 5 difference cell phone plans.

Students should take a few cell phone plans and compare the plans, including the cost for text messages (which may include similar graphs), the cost for extras, start up costs, etc…  I found the students end up needing to create piecewise functions in order to represent a cell phone plan which has a fixed rate until the minutes are used up at which point the customer has to pay extra for each minute.


Shape and Space: Design a new school building.

Here I showed the students the new lot our school is in the process of purchasing and our project is to design a building for that spot, and calculate how much their building design will cost (within the nearest $1000).  It involves finding area, volumes, perimeters, scales, perspective, etc… We are using Google Sketchup for the designs but I am now trying to work out how to import the students designs into a virtual world (like OpenSim) so we can have each student group lead walk-arounds of their building.


Polynomials:  Determine how many operations multiplying a 100 digit number times a 100 digit number takes.

Students are learning about computational complexity theory by analyzing the number of steps it takes to multiply numbers together.  They record each step in the operation and increase the size of the numbers of each time and re-record their results.  They then compare the different number of steps in each operation and try to come up with a formula, so that they can answer the 100 digit times 100 digit question.  Our object: Figure out why our TI calculators can’t do this operation.  It turns out that the formula itself is a polynomial, and their substitutions to check their various formulas count as a lot of practice substituting into polynomials, which was a perfect fit for our curriculum.


Quadratic functions:  Create an lower powered air cannon and use it to fire potatoes a few meters.

Here the students are attempting to use quadratic math to try and analyze their cannon, then the objective is to try and hit a target with a single shot later.  The cannons should be very low powered for obvious safety reasons, capable of firing a potato (or Tennis ball) a few metres at most.  There is also a slight tie-in to Social Studies where my students will be studying cannons in their unit on medieval warfare.


Bearings and Angles: Set up an orienteering course in your field or local park.

Students attempt to navigate a course through a park and pick up clues at each station, which they use to figure out a problem.  Students have to be able to recognize the scale on the graph, navigate using bearings, and measure angles accurately.  Also lots of fun, we did this in Regents park for a couple of years in a row.


Integration: Calculate the area (or volume in a 3d integration class) of an actual 2d or 3d model.

Basically you have the students pick an object which they then find the functions (by placing the object electronically in a coordinate system) which represent the edge of the object, then place the object in a coordinate system and calculate area of the object using integration.


Percentages: Find out how much your perfect set of "gear" (clothing) costs when it is on sale and has tax added.

Students take a catalog and calculate how much it will cost for them to buy their perfect set of clothing.  They can buy as many items as they want (with their imaginary money) but have to keep track of both the individual costs and the total cost of their clothing.  You can also throw some curve balls at them, like if they buy more than a certain amount, they get  discount, etc…


If you have any other examples of real life math being used in a project based learning context, please let me know.  I’m always interested in other ideas, especially for the more challenging areas of mathematics.  I’ll add more ideas here as I remember them.