The Box Problem Updated

Phew - finished correcting those Box Problems (see post from Sept 9th 2015). They were great. Really. But so time consuming to grade. And I'm efficient - been doing this for 25+ years. I have a system where I sketch out what each section should have and points for each part. Then I do the first item in the rubric for every student. Then the second item for every student. Then the third. And so on. This way I am consistent in what I am scoring and what comments I am making. Also I kept track of good responses to each part so I could share what a good response looks like. This all took about 6 hours. For about 45 projects in all. There goes my Saturday. (I did get in a hike and a little grocery shopping).

Of course when I correct any project/performance task I make notes of things to tweak for next year (or typos to repair). So what I posted on the 9th has been updated here.

One thing I added was a "Perseverance Score" on the rubric. Our math department is trying to integrate all the math practice standards into our work but one in particular is MP1:

CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

In particular my rubric states the following:

1)     Perseverence  - (math practice standard 1) Demonstrates ability to make sense of problems and persevere in solving them.

This standard states that students should be able to do the following:  Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They are able to transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"

                     In this first project students will be allowed one clarifying question but more                  questions and more direct levels of help will result in deductions on this section.

These honors students don't like this very much. They want you to tell them that they are doing something correctly. Overall though I only had a few students come see me before this was due. Everyone was in good shape and seemed pretty well prepared for this project. The scores were good. Not too many As. Lots of Bs. Because there is a tweaky little thing in the graph that the students think is in the problem situation domain but really isn't.

And students just aren't comfortable with "being suspicious" of weird behavior on a graph. They just assume since it is in quadratic I it must be part of the problem situation domain. But a few were curious and investigated and really understood that weird little bit.  I LOVE it.

My mantra this year with my precalculus student is to BE CURIOUS. Investigate weird stuff. And we've been looking at functions that do weird things (especially rational functions and piecewise right now). So that little section in this project emphasizes that.

When I hand these projects back, I'm going to go over each part (briefly!) and show them a "good" response. There were lots of good responses for each part. But I chose one and photocopied it (deleting anything that showed the identity of the student who did that response) and will show it to the class with my document camera. I'll do this for each part but then also post a pdf document of all the parts together on my web page that students can look it over. And consider their responses with respect to what I deem as good responses. (I don't want to post it here, just in case sometime in the future a students stumbles upon it and uses it to do their project. You never know. If a teacher is interested in this composite document, just send me your school email address and I'll send it off to you).

Hopefully this will help the students with their next project - Minimizing the cost of a soda can.

http://www.debbiewaggoner.com/math-practice-standards.html