Enviroment
Prior to meeting with the student I intended to use for the assessment activity, I asked Mrs. Beauchamp, a math teacher at our school, to administer a problem of her choice to a student in her 8th grade class. I thought it would be beneficial to me for me to observe. Time only allowed for one problem at the end of her 2nd hour class. I allowed her to choose the problem from Level "A" the appropriate level for the student being assessed. The problem she selected was from strand "M". It asked the student to put metric measurements in order from greatest to least. The student struggled initially with how to set up and convert. Mrs. Beauchamp gave the student hints and direct instruction via scaffolding. She told him to: (1) use a ratio box; (2) mm on top and cm on bottom; (3) when you divide by a multiple of 10, move decimal over once; (4) now that you've converted one to cm now you can do the other; (5) now take that down to meters; (6) how many cm are in 100? The student completed the problem correctly, but did have to put forth quite a bit of effort to complete this multi-step conversion problem. It was my turn next. I picked a 6th grade female. I met with her in my office during her gym time. I predicted that one hour* would be all the time I would be able to devote to this assignment; however, to do the assignment justice, I feel like much more preparation on my part was needed certainly! I had the math assessment cards laminated. I then cut them up and grouped them according to Level and Strands. I placed in front of her the problem sets grouped according to strands. I then asked her to pick one problem from each problem set. I included one problem set from Level "B" to satisfy the requirement of problems from at least 2 levels. The strands consisted of: 7 measurement cards; 3 data; 5 algebra; 5 extended; 9 number; 7 geometry. Her final strand choices consisted of 2 geometry, 1 measurement, 1 extended number, and 1 number.
*I predicted that one hour would be all the time I would be able to devote to this assignment; however, to do the assignment justice, I feel like much more preparation on my part was needed certainly!
Approach
I had the math assessment cards laminated. I then cut them up and grouped them according to Level and Strands. I placed in front of her the problem sets grouped according to strands*. I then asked her to pick one problem from each problem set. I included one problem set from Level "B" to satisfy the requirement of problems from at least 2 levels. The strands consisted of: 7 measurement cards; 3 data; 5 algebra; 5 extended; 9 number; 7 geometry. Her final strand choices consisted of 2 geometry, 1 measurement, 1 extended number, and 1 number. I did follow the suggested protocol. Questions that I asked consisted of: (1) How do you know your answer is correct? This is a divergent question. (2) Aren't there other ways to count to 10? This is a factual question. (3) Did you know that you need to change the sign and add? This is a factual question. (4) Can you go into more depth? This I would consider a convergent question.
*Had time permitted, I should have consulted her teacher to ask what areas of math this particular student struggles or excels in.
I couldn't explain the rule pertaining to changing the sign and adding. That bothered me. I had to draw a number line to show her instead.
Summary
(a) Strong mathematical concepts appeared to be: Measurement.and Geometry. She knew (1) basic units of measurement, i.e. 12 inches = 1 foot and 3 feet = 1 yard and that she had to convert the units. (2) She would then know that the whole is to the part as the part is to the whole. (3) She visualized quite easily the questions that were illustrated with the grids (2) whole numbers and proper and improper fractions.
How did I know? She was able to arrive at the correct answers. She also was able to convert a fraction into a whole number.


(b) Strong mathematical procedures: (1) conversions and (2) solve for an unknown (3) order of operations.
Which needed further development? She wasn't able to set up in algebraic format the solve for the unknown. She also did not know how to divide fractions and use the reciprocal. She did not know how to change the sign and add when working with negative numbers.


(c) I think she understood and was acquainted with what she knew she was supposed to do. I don't think she had a deep understanding though of why she was doing what she was doing. She knew basic steps.
How do I know? Her ability to reflect on what she had just done was challenged first by her level of patience; and, second, by her depth of knowledge as evidenced by her ability to relate it to real world application. But for her to acquire that skill and perfect, I would need to be more skillful in providing opportunities for her not only to create knowledge but to produce knowledge.
What activities would I do? I think by doing more data analysis projects of the problems the student just finished embedded into a culminating activity, the student would be able to make concrete connections, i.e. mental velcro. The book, "Empowering the Beginning Teacher of Mathematics", calls it learning math in an active manner.


(d) Mathematical connections and communicate mathematically? The student was able to relate mathmatically to a number line. I found it interesting that she appeared to want to solve the problems without setting them up and instead work them in her head initially. Maybe she sensed that we were in somewhat of a hurry.* But, even when she did show her work, she didn't go into a lot of detail.
Next steps in instruction? I would want students to show their work to prove they understood the procedures and, ultimately, the concepts. If the student doesn't understand reciprocals, then the student won't understand or perform correclty cross multiplying and multiples of numbers.
Activities: I went to Encyclomedia this year and set in on a breakout session conducted by a math teacher who uses guided math groups like reading groups. Once every other week, she groups students in groups of 4 or 5 and rotates every 13 minutes between 4 different centers. She uses math problems of the week concentrating on problems from the math specs. She uses math boxes. She uses everyday math games. She uses calculator activities, logic puzzles, brain-stretching activities, Versatilies*, and Sudoku.
*In order for her to develop a deeper level of understanding, I would need to design a unit that required a deeper more authenticate demonstration of knowledge. For example, I'm watching Elevators for Dummies on Nova. What a great topic to develop a unit around.

*I absolutely love Versatilies and have used them with my GT students who also LOVE them. Every teacher should have a set of Versatiles.

(e) Additional Activities: I would definitely use the Versatiles. The immediate feed back given the student is extremely gratifying and challenging, as well. Research shows the brain responds to differences, challenges, and images. Versatiles incorporates all of these cognitive functions. It's problem solving at its best.

Link to Photos
Link http://whitswiki.wikispaces.com/Assessment+Activity+Pg.+2