Academy of Best Practices: Day 2 Assessment

Today's focus was on assessment and team building (although I don't think that team building was the stated focus, it is just when I picked up on today.) We started the day by finding our teams using multiple representations of a linear function.  We each took a card and had to find matching representations.

Once we were in our teams we were given time to create certain three dimensional shapes with only a string, a picture and us as team members. I found this particularly challenging, since it takes me a little longer than think spatially (I also have impressively weak fine motor skills.)

We were then given a problem that was intended to challenge us to think and to stretch our own abilities to work in teams (dealing with an invented base (-4) and translating the first 25 base 10 numbers.) There were 4 parts with increasing complexity. To be honest, I struggled with not moving onto the next part of the problem. I really wanted to see where the problem lead, but I needed to take time to make sure everyone in my group could do the same.

Both activities gave me such compassion for the difficulties participating in group work. My group had to wait for me and pull me along during the string construction activity and I needed to not sacrifice staying with my group for the sake of the problem (the problem will still be there tonight.) I did experience satisfaction and shared excitement as we solve the problem together. Worth it!

We then talked about assessment and rubric building. We were given a problem as a team to work. Then we were asked to build a rubric together for this problem. This was quite a lively discussion. I was thankful I could contribute due to the many rubric discussions my wonderful 7th grade math team had last year! After this, we each took a stack of papers and used our rubric to grade them (I kind of felt bad for all the hard work students put in only to be graded by us and recycled later.)

Once we decided our score, we put it on the underside of the paper in the right corner and placed it in the center. After we each graded a stack, we took a stack from the center we had not already graded, but another person at our table had. We couldn't see their score and we graded it and put our new score on the top left underside corner, then flipped it to compare. If we disagreed, we put it in the middle of the table to discuss later. Our rubric was pretty precise, and yet we did differ on several papers.

Each paper led to a conversation and final score. Of course doing this for every problem would take forever, but one is doable. I really enjoyed seeing all different perspectives and totally missed one student's drawing and gave her a 2/4 when really, she completely understood and represented the problem in a way that was not immediately apparent to me.

Motivational: used to encourage, no guidance. Example "Good job" " :)"
(I use this quite a bit)

Evaluative: measure, score, numbers." -1", "21/25", "88%"
(Yep, I do that too.)

Descriptive: what needs to be done, "Read directions", "Calculate answer", "Check your work"
(Yes...)

Descriptive Effective: move them to the next level, should make the learner think. "How could you use the table/graph and chart to find the change in x and the change in y."
(Only rarely do I use this.)

Descriptive Effective helps students take the next step in learning. Again, doing this for every question would take forever, but we can definitely do it for a critical skill problem.

Here is our attempt at descriptive feedback.

We spent some time modeling strategies to use with groups to build understanding. Below is our on going list with arrows checking of what we have covered in two days.  I hope to revisit this list to add diversity to my team strategies.

We also used Algebra tiles to work with negative expressions and equations. We discussed how confusing the minus sign seems to be with students and all the definitions we use for this simple dash. I had never used a 4 sided mat to model inequalities involving negative and positive expressions, and found it very interesting to see how the opposite of a negative is positive using this visualization.

We ended class with a walk and talk with our "critical partner" (a partner chosen at random with the intention of collaboration about our action plan goal for the year.)The walk and talk is a strategy where you are given a topic and time limit and leave the room to walk and talk about it. It is lovely to get out of the seat you have been in for several hours and talk about the same thing you would be talking about at your seat. I must say, it does give me some anxiety to use this in the classroom.

I can't wait to see what tomorrow brings!

Academy of Best Practices: Day 1

Today is the first day of what a friend helped me label a "mathcation." I get to travel to a new place, go to dinner every night, and do a bunch of math and teacher training during the day. Personally I can't think of two things I'd rather combine! Today's focus was on grouping strategies and multiple representations.

One of our tasks was a remake of one I had done before. Given different sized circles, measure the circumference and diameter and record the results.  The primary goal is to allow students to find that the circumference is a little more than three times the diameter. Or said another way, the ratio of circumference to diameter is about 3.14 to 1. Today we created our circles in a way I had never seen before. We used bubbles! We were given some homemade bubble solution, poured a little on our desk, dipped a straw in the solution and blew a bubble on the desk.

We, of course, tried to create the biggest bubble possible. After the bubble popped, it left a circular mark on the desk. We were then given string and a centimeter ruler to determine the circumference and diameter. Of course, the teacher across from me talked about how to make the diameter more accurate, since the center of the circle was hard to find. She recommended we take an average of diameters within one circle including a length and width one. Yes, I thought to myself, this really is a mathcation with like-minded people who probably considers it one as well.

We recorded our results in a table, and then plotted them on a graph. I enjoyed using the sticky dots to represent our data point, and think students would feel the same way. Who doesn't like stickers?!

Then we were asked to calculate the ratio of our circumference to diameter. The results were recorded on the board. We got surprisingly close for the most part. I was off by quite a bit, with my inaccurate measuring skills due to frustration with a wet string and unimpressive fine motor skills. I think I calculated 3.4.  Luckily, the activity compensates for the butterfingered participant and we averaged the results and got around 3.2. Pretty impressive using bubbles and string.

What I really liked about this activity was the graphical representation. It connects rather nicely to the line of best fit, proportional reasoning, and the meaning of slope (about 3.14 in circumference over one diameter). What a lovely unit rate!

Even though I have seen an activity like this before, a new twist was exactly what I needed to be able to connect this discovery to many more mathematical concepts. I can't wait to blow bubbles in class!

This is just a snippet out of my day. Looking forward to more tomorrow!

We were given quite an interesting homework problem to discuss tonight: Very Woodstocky for the young crowd I am surrounded by who probably think of Woodstock as a bird (or maybe not even that!)  We also have some reading to do tonight, so I will most likely finish that first and save the problem for homework dessert!  

Solve this math problem: A rock festival was attended by 50,000 young people, 24,000 boys, 20,000 barefooted, 27,000 listening to the music. If there were 12,000 barefoot boys, 10,000 barefoot listeners, 11,000 boys listening, and 4,000 barefoot boys listening, then how many barefoot girls were there? How many shod boys not listening?