What's wrong with traditional math assessment?

Ever since my first experience as "the teacher" in a classroom I've always felt uncomfortable with the way we traditionally assess math. The traditional unit exam breeds last minute cramming and memorization of procedures and questions by the student. This is followed by an all to common brain dump of useless information (i.e. math content) about 10 seconds after they hand in their exam. There must be a better way. Now after reading a post from a student on Students 2.0 it seems as though some of the students feel the same way!

Students 2.0 via kwout

Could this be the sparks of something new burning in the future of teaching and assessing of mathematics?
Personally, as I went through my university career I learned that I would never memorize all the questions that could be asked or all the different scenario's that I could possibly encounter, but what I could do is understand the principles and key ideas underlying all the questions and thus be able to apply those understandings to whatever I faced on the exams. Ironically enough it took less time to study this way then it did when I tried to do one of every type of question I might face. This discovery didn't come until about my second year of university, which was preceded by my k-12 schooling, two years at a technology school, and a year of university classes...oh the wasted hours memorizing and agonizing over all the information to take in.
Now with this new found outlook and a desire in our students to want to be tested more meaningfully I feel the time is now for something new to develop. There is a difference between knowledge and understanding. Wiggins & McTighe have a great book out called, Understanding by Design, that explains this idea and how we can design our teaching and assessing to facilitate understanding. Closely related to this is the idea of Bloom's Taxonomy, which was published back in the 50's but wasn't very popular until recently. The idea is to get students to think about the content (no matter what it is) and to bend it, twist it, shape it, and make it fit into scenario's, contexts, and applications that differ from what they have seen it in before. Basically we are looking for the student to demonstrate the ability to transfer knowledge across into other areas or applications.
In math this may come about as problem solving, projects, presentations, or research into real life applications. I have found one great resource on the net that has a collection of great higher level mathematical thinking objectives involved in the assessment tasks. It was put together by Harvard graduates from 1993 to 2003 (a fairly credible source, don't you think?). Here is the link.
So as I make my way through this crazy world of teaching I learn from the past, refuse the status quo of the present, and anticipate change for the future of education.

Hired to teach?

So the high schools are writing finals this week, thus, me being a substitute, will probably be having the week "off". Being a recent grad and getting letters in the mail that have big sums of money owing on statements that come from the banks and various loan agencies is not a real happy thing. Plus, it is a balmy -45 degrees celcius today...not a real good start to the week. Then after lunch I get the call..."Hi Tyler, this is so and so at THE high school. We would like to offer you a full time teaching position for the second semester." As I try and sort through what has just been said to me the principle goes on to describe what comes next in the whole job offer process.
With a baby on the way and my wife due to go on maternity leave next week you could say, perfect timing. And now the sense of satisfaction as my child starts its life I can look it in the eyes and not feel like a dead-beat dad and actually support my family (wow, who would have known getting that University degree and racking up all that debt would have paid off so soon).
My issue is this. I am hired on full time for next semester. I will be teaching four classes in a school I have never been in, to kids I've never met, with staff I don't know and here's the kicker...I don't even know what the classes I am teaching are yet! I must have missed the how to teach a full load with no prep time class at university. The old sink or swim...ahhh isn't life grand. All I can say is I am grateful for the opportunity and hopefull that there will be some helpful people at the school I will be teaching at. Let the mayhem begin!

Students teaching students

During my internship I was having a discussion with one of the teachers in the math department and she described a situation that she had with her grade nine math class. Basically they took the students from one class into another class (same grade and subject) and basically they had the students from one room be the teachers to the students in the other class. So peers were teaching each other. Below is the description from the teacher involved.

"My grade 9's had already completed sections on adding/subtracting with polynomials. I had introduced them to alge-tiles as an aid to do this. I made sure all my students were comfortable using the alge-tiles. The other gr. 9 class we went into had not started this section, so I matched my students in pairs making sure the pairs complemented each other as far as ability. Stronger with weaker etc. I prepared a teaching guide sheet for my students to make sure they taught all the concepts to their group. The learners(Gr. 9's who had not covered the material) had worksheets they had to complete to show their understanding of the lesson. Each group had 2 teachers to 3-4 learners. Some of my teachers were not ready to take on this role as they had not completed their assignments so they worked on those in the same time period. Alge-tiles were given to each learner. It was most impressive how on task 50-55 Gr. 9 students could be all in the same classroom. We had used a science lab so there was lots of room to spread out. I had numbered all the work spaces so I assigned my teachers to an area and the other teacher assigned his students. We had agreed to place my strongest teachers at stations were they would be matched up with his weaker students. I used 8 stations. The students enjoyed the activity and accomplished the objectives. We hope to reverse this process at another point in time where the teacher/learner roles will be reversed between the two classes."

From the responses that the students had and the excitement that the teachers showed from this activity makes me hope that I might get to try this idea out for myself someday. As we all know, teaching something is the best way to learn it and I think that the students that get a chance to experience this for themselves is very powerful for their understanding and long term storage of the material.

So simple

" I have no special talents. I am only passionately curious."

-Albert Einstein-










If we do nothing else but instill this in our students are we not successful?