Tuesday, April 23, 2013

What's wrong with Math Education?

"You can't teach that now, because then what am I going to teach next year!"

Ever heard this?  Ever said it?  Ever been a part of a conversation with this used?

I know I answered "Yes" to all three.  When curriculum is designed linearly, then we encounter such problems.  You have to know Y before I teach you X.  However, what if curriculum was designed around the questions student asked in class?

In two of my classes this year, I have eliminated "Units".  I can now demonstrate how math flows from one concept to another instead of teaching through 5 disjoint units, and no longer do I have to answer "You will learn that later"

Check out the clip below

Friday, April 19, 2013

How I abolished grading.

Here is the story of one teacher who abolished grading in a highschool calculus class.

I started teaching highschool Calculus at my school a couple of years ago.  When I started teaching the course, I used a traditional assessment strategy.  I would assign homework daily, end the week with a quiz, and then end the unit with a multiple choice/written exam.

My classes would start around 30 students, and by the end of the semester the class size would be 20.  What I did was "weed out the weak".  One day I realized that I wasn't weeding out the weak mathematicians, but instead weeding out the weak test writers.

This year, after many talks with first year University and College professors, administrators, teachers, students, and parents, I am proud to say that I have abolished grading.  We are currently in the middle of our semester and I have not graded a single item of student work.

Before you continue, I want to remind you that this does not mean I have not assessed, but not one student in my Calculus classes has received a grade at this point.  (Other than the report card mark which I must give).

How does it work?

First, I went through my outcomes, given to me by the government, and identified what the "Rocks" are.  These rocks are the outcomes which I expect the students to master above all other outcomes.  I chose these certain outcomes after my discussions with others and as well as what will be helpful for students to succeed in the future.

Next, these outcomes were rewritten in student friendly language and then provided to the students on the first day of class.

My teaching schedule did not change, nor did the speed on which I have taught the course, but what has changed is the speed at which the students can learn at.  Once I had taught 2 or 3 outcomes at a level where I felt that the class has mastered the outcome, I administered a summative assessment.  For this assessment, each child wrote it as a traditional exam, but it looked drastically different than a traditional exam.  Each assessment was entirely written, broken up by outcomes, and tested only the basics of the outcomes.  There were no "trick questions", just simple questions that would assess "Can the child demonstrate this outcome, on their own, as a basic level of understanding?"

When I assessed these assessments, I would write comments only on them, and either a "Outcome demonstrated" or "Need to learn" for each outcome assessed (Not on the overall assessment).   It is very important to understand that "Outcome demonstrated" is not a 100%, as a student could make a minor mistake and still achieve this, as I am assessing understanding the outcome, not perfection. 

Next, if the child received a "Need to learn" he/she must do the following:
1) Demonstrate the understanding of the questions given at a later date.  This usually occurs after a lunch session, a quick conversation, or multiple conversations with the child.
2) A conversation explaining how he/she made the mistake earlier and how their understanding has changed now
3) Write another assessment on the outcomes.

If after completing these 3 steps, he/she can demonstrate the outcomes then I would I count this as "Outcome demonstrated" just as if the child had done it the first time.  I do not deduct marks based on the number of tries needed.

If the child still does not demonstrate, (which is extremely unlikely as I have seen) then he/she must repeat the same 3 steps.

After 5-7 outcomes have been taught, then each child is assigned an open ended project.  This project consists of each student creating a problem around the math in the 5-7 outcomes and solving it.  The expectation is the problem is one which is deep, relevant, and for a purpose.  This part is not always easy! 

An example:  A student to demonstrate his understanding created a Call of Duty video and determined the rate of change of a ballistic knife falling in the video. 

These projects usually range from 3-5 pages and must be handed in individually, but can be worked on with assistance from others and/or textbooks.

To assess these projects, I follow the same pedagogy from above.  I use comments only, and give guidance towards any errors I see.  The projects are then handed back to each student, who can go back, make corrections, and rehand it in.  This process is repeated until the child receives perfection on the project.

I have even abolished the traditional final exam.  The expectation is the students must give me a 30-45 minute presentation around the rocks of the course, and demonstrate their understanding of all rocks. 

How do I get a final mark percentage?

I simply take the number of outcomes and projects completed (at the end of the course) and divide by the total number of outcomes and projects.  This is not the best strategy, but it seems to work for me at this moment.  I do weigh projects twice as much. (I have 20 outcomes, and 5 projects, so the total is (20+5x2=30)

Here is my updated list of rocks. 

Let me know if your thoughts

Wednesday, April 17, 2013

Student led in High School.

This now sparks the third pair of interviews where I didn't bring any grades into any conversations with parents.  I have been asked many times how I do it, below is one experience of how I did it.

Parent: How is my child doing in your class?

Me: He is a hardworking student, seems to really enjoy hockey, and how the statistics of it relates to the course. He has, however, struggled with relating the combinations of the way teams could be arranged in a tournament, to the ideas of the course..  I believe that he has demonstrated superior knowledge in how a graphical representation of the scores of team can be manipulated through transformational change.

Parent: How does he rank with the rest of class?

Me: Well he is at the top of the class, but honestly this is the weakest class I have ever taught.

Parent looked puzzled.

Me: I am not being entirely true.  When it comes to your son's interest of hockey he has demonstrated an understanding of it far superior than any other child in the class.  See, the rest of the class doesn't share this passion and interest of hockey and finds it hard to understand the applications of it.  Jim has demonstrated a keen ability to relate this passion to many assignments, and questions we have completed in class.

Parent: Ok, but on the report card his mark is XX%, and what can he do to increase it?

Me: What mark should Jim receive?

This is when Jim smiled and he said "100%".

Me: Awesome, now what have you done to demonstrate a full understanding of the material.

Jim: Well I completed a ---

I interrupted him and asked him not to tell me but his mother who originally asked the question.

Jim: ok... (now a little shy) mom I graphed a function which shows how the Calgary flames is not increasing over time (I laugh) Quiet Mr. Martin I am talking...

And then I listened to Jim explain to his mom about what he did, what he struggled with, and how he wants to go back and ensure mastery of all concepts. 

**I do have to give credit to another teacher, who minutes before messaged me about how she is giving student led conferences and I wanted to try one immediately**

The result was amazing.  The student took control, and marks were not the focus but his passions, interests and his own challenges were. 

I then explained that I am willing to reassess him if he does truly go back and learns the material for which he struggled on earlier.

Info about standardized tests

I have been asked many times if I will allow my own children to write optional standardized testing, which in our province we call Provincial Achievement Tests. Before I make a decision, here is some information about standardized exams.

First I would like to discuss the Evidence around standardized testing.

- The effectiveness of standardized testing as a means of improving education has been widely questioned and critiqued in the relevant research literature. Standardized assessments have not been demonstrated to improve teaching or learning in any significant manner (Hout & Elliott, 2011).

- Standardized assessments provide one-time snapshots that do not accurately measure how a student performs day after day and they are, by their very nature, summative, rather than formative. Teachers who perform regular assessments daily are best positioned to evaluate how a student is performing vis-a-vis curricular outcomes (Davies, Herbst, & Reynolds, 2008; Harris, Smith, & Harris, 2011; WNCP, 2006).
- Standardized testing diverts teaching time and monetary resources away from student supports, teachable moments and direct teacher-student contact time (Kohn, 2000, 2011; Sahlberg, 2011).
- Provinces including Alberta and British Columbia (Steffenhagen, 2012), as well as several American states (Bryant, 2013), including more than 600 schools in Texas alone (VASS News, 2012), are scaling back from standardized testing, opting instead for the less pedagogically harmful and less costly random sampling.
- Standardized tests are often culturally biased against those for whom English is an additional language, and have been demonstrated to be more reflective of depressed socio-economic neighbourhood conditions (Abedi, 2010; Sawa & Bouvier, 2010; VASS News, 2012), than the quality of teaching or learning of teachers and students.
- The results of standardized tests when published in newspapers carry negative side effects, including a significant drop in student and teacher morale (Paris & Urdan, 2000).
- The Finnish "fear-free" school system that eschews competition, failure, and standardized testing regularly tops the 34 countries tested by OECD's Programme for International Student Assessment and several provinces who have mandatory standardized testing perform less well than Saskatchewan on the same PISA tests (OECD, 2010).
- Many children experience increased anxiety as the standardized testing date gets closer and especially upon testing days (Gail Jones, Jones, & Hargrove, 2003; Segool, 2009).
- Standardized testing runs counter to the ministry's stated goal to improve retention and graduation of aboriginal students, since these tests often serve to further marginalize and push out students who are already vulnerable (Crandall & Kutz, 2011).
Next, I haven't found one, single, research based, reason to support using standardized testing before grade 7.