CCTM- Diagnosing Secondary Students' Conceptual Gaps

presented by Glenn Bruckhart and Bernice German of the consulting company, Peak Achievement
By far the most power presentation. And who doesn't respect Glenn Bruckhart and his work?
The team of Peak Achievement is working on helping teachers better assess their students, interpreting these assessments to identify conceptual gaps and providing professional development on how to fill them. The documentation they provided was from a 9th grade pilot with previous low unsatisfactory scores on CSAP. After 5 months of working with Peak and receiving grade level instruction and peak's intervention program, over 45% of students moved one or more grade levels. The class averaged a gain of 45 points when the state's average was a 14 point gain.
The biggest conceptual gap that they identified in these 9th graders was subtraction. Everyone was shocked that it went back that far. The big takeaways:

• The assessments they used to see where the students are should not measure what they can do, rather, how they think. The example assessment not only asked student to solve a addition or subtraction problem, but to explain their thinking in words or pictures. (contact me for copies of the material from the presentation)
• Students had trouble with subtraction and division which may be connected to the fact that they are the non-commutative operations.
• Students start math at counting. They start with concrete examples. Ideally, it moves from counting concrete examples to using numbers to represent these concrete objects. This representation is then used in operations which goes into abstract concepts. If we don't use this sequence properly to move students from concrete to representational to abstract thinking, they don't really understand the concept and may or may not learn the algorithm. That is not enough to build on with higher math.
• The example we did at our tables is take 46 popsicle sticks and bundle groups of tens with rubber bands. The four bundles represented the four in the tens column and the 6 loose sticks were the 6 ones in the ones column. We were asked to take away 19. This required unbundling at least one of the groups of tens. Unbundling them clearly kept the idea that the bundle was a still ten popsicle sticks. We were representing the problem 46-19 with concrete examples. The words "take away" 19 is directional which may help students understand that starting with 19 and taking away 46 is different. It would be better to use this directional and concrete language rather then minus, subtract or even borrow (from the ten's column).
• Students should be able to recognize what numbers are referring to. The assessment item asked what is 12 apples + 25 oranges. Students who answered 37 should be asked 37 of what? This is directly relatable to algebra when student should know that 2 + 3x means two of something and three of something different. This also can help students to identify useful and non-useful numbers in word problems. It is assessing how well students have bridged from concrete to representational thinking. If they don't understand what numbers are standing for, they can't really do the math correctly, unless they get lucky.

I did speak with with both presenters and Bernice would really like to work with our district. I explained that our PL set up is moving away from inviting outside experts come work with us. They are working with another district to provide PD for some staff and having them go back and relay it to their colleagues, so they may consider that option for us, if we ever get to that point.

First, I know that the concentration of most efforts and energy right now is trying to set-up the curriculum to avoid such gaps and I agree that it is important to get out of reactive mode and into proactive, quality first instruction mode. After that is complete, we can work on such interventions. However, I really think that we could use the experts within our district to provide a similar intervention. The key is admin buy-in and are we ready as a school/district/community to acknowledge such gaps? What do you think about some of the ideas in the presentation? What type of gaps would you guess some of our struggling students have? Do you think something like this would be worthwhile? How do you think the students and community would react if we found similar gaps and provided similar interventions? What types of gains would you predict?

CCTM- Proportional Reasoning

presented by Jimmy Frickey and Russ Rendon, Eagle Rock School based on chapter of John Van deWalle's book Elementary and Middle School Mathematics, teaching developmentally.
Even if the title suggests otherwise, I think this may be one of the most important books I should read to be a better high school math teacher--as judged by student success. I'd like to see if we have any copies available through the district and if anyone else is interested in doing a PL book study--all contents included.
Takeaways:

• Proportional reasoning is the cornerstone of Algebra*
• A key developmental milestone is the ability of a student to begin to think of a ratio as a distinct entity, different from the two measures that made it up.*
• Elementary focuses on relationships resulting from adding and subtracting whereas proportions involve multiplicative relationships.
• Proportional thinking is not "cross multiply and divide"
• Proportional thinking is recognizing direct and indirect correlations, quantitatively and qualitatively.
• Proportional thinking is evident in fractions, similarity, indirect measurement, data graphs, probability, percents, rates, linear relationships, trig and many more math concepts as well as other contents. Proportional thinking is in many science topics, including biology and chemistry, art such as mixing colors on a color wheel in different proportions to determine the desired color, health since there are so many rates involved, economics, including unemployment rates and interest rates, social studies, such as currency exchange rates, bad press vs number of votes, allocation of resources-is it proportional? etc...
• Incorporating Proportional reasoning in other subjects can enhance most other contents.
• It is estimated that more than half of the adult populations cannot be viewed as proportional thinkers.* It might be interesting to have the students "quiz" other teachers and staff so and start a community initiative, so they students feel not so alone in the endeavor and appreciate its importance in seeing other adults make efforts to learn it.
• Premature use of rules encourages students to apply rules without thinking and, thus, the ability to reason proportionally often does not develop.*

*Taken directly from copy of John Van deWalle's book.

What do you think? Anyone interested in a PL book study? How can we get this message across to the whole school or community?

CCTM- Learning to Read Mathematics

presented by Sharon Benson
Mostly elementary and middle school based concepts and strategies. What I took away

• Students skip to pictures/diagrams and guess what they have to do to solve the problems, especially second language learners
• Sometimes text is misleading, sometimes pictures/diagrams are misleading especially if different than what students pictured when reading text. The conflict makes them shut down and not attempt a problem
• ESL students get the big, important, explicit vocab words but need help with the little words
• Ask students to highlight words/phrases/diagrams that they don't understand to visually see what the roadblocks are for students. May use this to ask students to exchange papers and have another student try to rewrite highlighted parts in their own words. If both students don't understand it, they may be more willing to admit it to the teacher and ask for help.
• foldable for Frayer model to help kinesthetic learners organize vocab components
• color code your word wall into categories makes a word wall even more useful
• constantly use formal and informal vocab at the same time as a behavioral pattern of teacher--students pick up on our patterns and will start to do the same, thereby increasing their vocab. Ex. Remember that the diagonals of a kite are perpendicular, cross at 90 degrees, perpendicular. The more we repeat, the more it sticks.
• As last part of problem solving process, have students restate what the problem was in their own words, this helps them recognize if they've missed anything
• There is a graphic in my notes about layers of word problems with what the question is asking on the outside and the solution on the inside. A good exercise may be to give them a number (solution) and have them work backwards through the process to eventually come up with their own problem. This makes them more aware of each step. When they feel confident with each step, they may not be as intimidated by going the right way. I may need to demonstrate this with a screen capture later :)

What do you think?

Laptop Cart more hassle than what it's worth?

Hi guys, I gotta do a little venting here cuz this is getting frustrating. This math cart is great to have but with only 15 computers im wondering if it is more trouble that what it's worth! When students are sharing a computer they are busy talking and not listening to instructions and then I have to repeat myself to each group over and over again. The gizmos must be done in pairs instead of individually. I also tried to have them print documents from my web page to find that not all laptops have printers installed.

Today has been a disaster with my first two blocks.

Students dont remember their passwords, not all have gmail accounts yet, gmail and google dont work together without setting up a google account. It's taken almost the entire class periods to just get set up and logged on to the gizmos! Im also finding out that these students aren't as tech advanced as we might think. Yeah they can use cell phones, but when it comes to links and sites and passwords etc.. they are lost. I know this all takes time and in the long run is worth the trouble, but the hard part is trying to fit this in with our curriculum time constraints. In trying to do a lesson on circles through the gizmo, i have actually wasted a day. I think it's just faster and easier to project it on the board and work as a class then as pairs or groups. But that is the same as we have always done it. Any suggestions or ideas?

Im gonna try it again for my last two classes today. Lets see how it goes.

Principals Common Assessment

Thanks to Regina Stewart and Jennifer Svihlik for helping create the Principals common assessment. I currently have the original and will make copies for the 8 sections of principals. I'd like to test tomorrow (9/20) because we pushed back the test from today for maps testing and that thursday is the only day we had available. Anybody got spare scansheets to share?

Geometry Classes

Hi guys, I've created a quick reference document for some of the conjectures we pass over quickly in Geometry. The ones about angles in Chapter 2. Students can print it and use it in class. It's posted on my blog site Gee-Im-A-Tree.

Also there is a good Gizmo lesson on Area of parallelograms and triangles. It has some cool animations and shows the relationship between are of rectangle and parallelogram.

Dept update

Alright Math Gurus, here's the skinny.

LAPTOPS
We have a MATH DEPT laptop cart with LCD, printer and wireless access point. Please contact me if you'd like to use it - maybe a wiki or something later.

ASSESSMENTS
According to the curriculum guides on starnet, we are all supposed to be testing on Wednesday 9/12. At the department meeting it was decided to push it back to Friday 9/14. No discussion was made about grading, or when copies would be made available to teachers for their classes.

MATH MATES
9th and 10th grade teachers, you should be using the "math mates" worksheets in class. If you have questions see me. If you have extra or need more go to SW200 closet.

INVENTORY
If you still need calculators - Tom Deaguero is keeping track of those, please see him in W202 to check some out. I believe he's got the graphing calculator and only the CSAP calculators are otherwise available in Regina's room SW207.

If you have textbooks I still need each number from you and your calculator count, please.

There was dicussion about the Pre-calc books, and ordering more. If you're teaching this class, or might be (Anatoly, Heidi, & Tom), can I get an estimate of how many we need to order? Also, the geometry books look pretty bad also; however, there's a closet full of them.

BUDGET
Mr. Paxton went to bat at the last board meeting and got our copy budget back, so we'll up the reimbusements on supplies to $200.

Don't forget to participate in the blog
http://achsmathtech.blogspot.com/

and the wiki
http://acsd14technology.wikispaces.com/