Main Ideas for Standards (Model with mathematics & Look for and express regularity in repeated reasoning)

 Standards

Read the material in the CCSSM Standards for Mathematical Practice and the PLC

articles on Sakai about your standards. Be sure to pick out the 2 to 5 important points about

the standards - and put it in your own words. Make a blog entry regarding the standards

that you have read about so that you and your partner(s) can see what each of you believe

is important.
 
4. Model with Mathematics

-Students can use prior math to help them solve problems in real-life situations
-Students can identify the important variables in a situation and draw out their relationship (i.e. diagrams, 2-way tables, graphs, formulas, flow-charts, etc. /or physical or pictorial manipulatives and symbols), and they are able to interpret, reflect upon, and understand those relationships.
-The goal is for students to become more skilled in mathematics
-Teachers can question students after they found a solution in order to have students determine if their solutions make sense within the context.

8. Look for and express regularity in repeated reasoning

-When computing calculations, students are able to identify repetition and generalize methods or shortcuts for procedures
-Students are able to evaluate/check their results to see if they make sense/are reasonable
-Teachers often simply instruction/provide shortcuts too early. It's important that teachers provide examples for students where they are able to identify regularity and answer questions where they can express the process they used (define their reasoning/methods).



PLC Articles 
 
Next, each member of your group is to read a recent article related to the Standard of

Mathematical Practice assigned to your group. Each person must choose a different article.

You may find these articles in the earlier NCTM journals. Use your email to let your

partners know what you are reading – early so they do not read the same material, each

person must read a different article. Use a blog entry to explain the material and examples

from your article. Now you make blog entry about the journal article - as a new entry for

the article on your blog.

1. Model with Mathematics 

Article: Spotlight on Math: Strategies for Addressing the Most Challenging Math Standards – Modeling

http://gettingsmart.com/2015/03/spotlight-on-math-strategies-for-addressing-the-most-challenging-math-standards-modeling/

Summary:

• Model is a representation of a real-world object or situation
• Not one correct model, but rather, there can be many models
• Ex. Numbers/symbols, geometric figures, pictures or physical objects, diagram (i.e. number line, table, graph)

• Teachers should ask/question students to explain their work and to relate it back to the original problem context. This way, students are constantly looking for connections/making sure their results are logical/make sense.
• Students need to use modeling to apply their learning on a regular basis. They need to look at real-world situations, identify a problem, collect data, devise a mathematic expression, check data, and revise.
• Modeling steps (may or may not be sequential):

• Identify a problem situation
• Make a representation of one or more elements of the situation
• Create a mathematical expression
• Compare results or predictions from the mathematical model with the real situation
• Make revisions to the model if needed

Examples:

• Bar diagrams to represent contextual problems requiring multiplication or division
• Using rectangular block diagrams to represent/solve problems with content from addition of whole numbers to ratio and proportion
• Making a presentation about area/perimeter of a school to prove school is too crowded.
• Book model (ex. adding 9 books and 15 books)
• Weather forecast models to predict weather

2. Look for and express regularity in repeated reasoning

Article: Reason Why When You Invert and Multiply

http://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/Blog/Reason-Why-When-You-Invert-and-Multiply/

Summary:

• Students need to reason in math. They need repeated practice to reach realizations/discover patterns.
• Teacher's should guide students in their understanding of how problems make sense.
• Students need time to explore what something means. They should know why we do that. (i.e. What does it really mean to divide by a fraction?)
• When teachers and students explore a problem, students will likely identify a pattern, which the teacher can then explain (i.e. reciprocal) 

Examples:

• Fractions
• They should know why we do that. (i.e. What does it really mean to divide by a fraction?)
• Students can recognize what a problem is really asking (i.e. What does 30 divided by 3/4 really mean? or What does it mean to divide two fractions?). Students will note patterns/new terms and actually understand the problem versus just applying shortcuts. In other words, shortcuts/generalizations are a great tool, but students should know what these shortcuts mean.