New School Year, New Blog

Welcome to Adams City and Welcome Back to another school year at Adams City. By building a strong community within our math department, we can all grow and the students can find sucess. Let's use this post as a test for you all to comment on and practice with the blog.
What's your favorite part about being a math teacher? My favorite part is that I get to make corny math jokes ALL day long and students just shake their heads! It's even better when a student makes a math joke!

CCTM- A Framework for a Balanced Math Program

presented by Carla Haas, and Julie Schmatz, Mesa County Valley Schools District #51
Mostly based on Five Easy Steps to a Balanced Math Program by Larry Ainsworth and Jan Christinson
The concept was intended to not be a new Math Program, but a framework to teach the existing curriculum and bring in components to help students be more successful at Math. I have a big packet if anyone wants copies of a presentation and some excepts from the book.
The five steps are

• Computational Skills (math review and mental math)
• Problem Solving
• Conceptual Understanding
• Mastery of Math Facts
• Common Formative Assessments

The main takeaways

• A portion of each class should be set aside for reviewing math concepts and skills that they had already learned and refine their number sense. Their structure seemed very similar to our Math'sMates, only Math'sMates has done all of the work of writing the problems and structuring it for us.
• The mental math is asking them a series of questions with integer or rounded numbers which sharpens their arithmetic skills
• Problem-solving as defined by NCTM Principles and Standards involves "Engaging in a task for which the solution method is not know in advance...and should be encouraged to reflect on their thinking" This seems to be more about strategizing and reflecting rather than the computations to get there. I think we all hope that the computations are the easy part of the problem solving for our students. Judging whether something is a reasonable response is also an essential part. I think this fits with our Take 5 program
• Conceptual Understanding is different than the procedural understanding. The focus should be on the conceptual understanding, which I'm sure most teachers strive for, however, I'm not sure we (me included) put the emphasis in the amount of time we spend on the conceptual vs. procedural. What do we spend our time teaching? How do we teach conceptual instead of procedural or more than procedural? How do we know if they get the concept rather than the procedure? What do we do if they don't get the concept?
• Memorization should follow instruction of conceptual knowledge--this produces mastery of math facts
• The use of patterns is most useful in helping students discover and emphasize the patters in our number systems. Building on previous math facts that they know, provide daily practice, and hold students accountable--including asking for parents support
• Commom Formative Assessments--As described by Ainsworth "They provide participating teachers with the timely feedback needed to differentiage instruction and thus better meet the diverse learning needs of their students." How can we restructure our curriculum to include so much cummulative review? How do formative assessments fit into standards based grading? Our current common assessments are not formative, they are summative. If we want to change our curriculum so that these assessments are formative, what changes need to happen in the pacing and structure of the units and what changes have to happen to the tests? Is MAPS used as a formative assessment? What about upperclass?
• These assessments should be designed collaboratively, classroom (individual--non-common?) end of unit assessment and scoring guide should be designed to match the common formative assessments
• The assessments should be scored and analyzed in data teams.

I would bet that these books have been a heavy influence in our current curriculum and assessment development since I have heard alot of the same language in our curriculum and assessment meetings. Anyone interested in a book goup?

Anyone interested in a book

CCTM- CoMMIT

presented by Jim Hogan, Aurora PS, Melissa Colsman, Cherry Creek PS, and Rachael Coulehan, Aurora PS
CoMMIT stands for Colorado Metro Math Intervention Team (or something very similar). Glenn Bruckhart is participating as well as many other concerned about math and math interventions.
Most of the presentation was around RtI as outlined by CDE.
Most schools have issues with students struggling with Math. This is an informal group that is meeting to discuss the issue and start to collaborate around why this is an issue and what can be done about it. The first thing that was identified was to develop common vocabulary around RtI, general and special education, and math program since the group includes such broad spectrum of participants. Currently, this group is still forming, gaining common vocab and identifying what the questions are. Most interventions discussed at the presentation were not possible due to other factors such as limited district resources, cumbersome such as involving so much paperwork, and unrealistic such as pulling students when there is no time to pull them. Even though there is a lot of ground to cover, it was exciting that this group is working on math interventions with no other political or hidden agendas--everyone just wants to help get students be successful at math.
The next CoMMIT meeting is on Dec 4th from 8am -11am in Littleton and Math on the Planes is scheduled for February 29th and March 1st with CCLD, Coordinated Campaign for Learning Disabilities. For information about these upcoming events contact Rachael Risley at rarisley@aps.k12.co.us

cctm- TI applications

presented by TI rep wgarciano@ti.com, more info at TI's educational website.

• Demoed some of the applications on the TI-84 plus silver addition.
• There is an application to graph inequalities and within that application is a way to graph a vertical line, i.e. X = 3. The other calculators only graphed functions of Y. This X= screen is only available with the inequality graph.
• There are pdfs on the sites of each application that describe the nuts and bolts for students to use it.
• The transformation graphs application looked very useful since that is a hard concept for our students to understand. This application allowed the parent function to be graphed and the constants manipulated manually, or run through an animation that showed dynamically the affects of some of those constants in transformations.
• Looks worth spending some time on students after the initial concept is taught. These calculators are allowed on standardized test such as ACT, AP and IB tests so hopefully this can help.

I am interested to see if these tools help. Maybe some action research within the department so see if they get a better or worse grasp on the concepts and how it helps with problems solving and/or test taking? Anyone interested?

In addition, there is a free TI-Nspire workshop at :

Littleton Education Services Center, 5776 Crocker St., Littleton CO 80120 on

Saturday, October 27, 2007 from 8:30-noon

Register by email asummers@lps.k12.co.us and include name, school, and district

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?