|It's all about process. The student must explain the method in solving the problem. Now the student will talk about the problem with the other students. It's the standards requirement.|
SBAC (Smarter Balanced Assessment Consortia) weekly update #65 includes information on Illustrative Mathematics Project, which is developing resources to support implementation:
Chaired by Bill McCallum, professor of mathematics and another contributing author of the CCSSM, Illustrative Mathematics provides guidance and develops resources to support the implementation of the standards. Through the website (http://illustrativemathematics.org/), the project has developed hundreds of tasks that illustrate the meaning of each standard and provide instructional best practices for teachers. This project aligns well with the Smarter Balanced vision of formative assessment practices that continually inform teaching and learning.
Here's a sample lesson in Common Core from Illustrative Mathematics:
1.OA Find the Missing Number
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Find the missing number in each of the following equations:
Commentary: This task asks students to solve addition and subtraction equations with different structures so that they are able to see the connections between addition and subtraction more easily. Examples should be presented with the the sum or difference on either side of the equal sign in order to dispel the notion that
= means "compute."
We know that if we subtract 3 from nine, the result is 6 so the missing number in the first equation is 6. The first equation should look like:
9−3=6We can either count up from 8 to 15 or subtract 8 from 15. In either case, the result is 7. The second equation should look like:
8+7=15We can ask, “What number do we need to subtract from 16 to get 5?” or “5 plus what number is 16?” In either case, the answer is 11. The third equation should look like:
16−11=5We know that if we subtract 2 from seven, the result is 5 so the missing number in the first equation is 5. The first equation should look like:
5=7−2We can either count up from 7 to 13 or subtract 7 from 13. In either case, the result is 6. The second equation should look like:
13=6+7We can ask, “What number do we need to subtract from 14 to get 6?” or “6 plus what number is 14?” In either case, the answer is 9. The third equation should look like:
6=14−9We have found the missing numbers in each of the given equations.
Look at the last equation and answer.
Here are my questions if I chose to log in and comment to "Banjo Ben".
- How much money are taxpayers on the hook for these new math standards? There's a wrong answer in that last equation that's cost a lot of money to prepare at taxpayer expense and no one has caught it in 5 months.
- How could an assessment company, the commenter and the website master miss such an easy answer?
- If the computer reads the pre-loaded computerized answer to the question, even though it is incorrect, will the student be graded incorrectly...for the correct answer?
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
What is particularly troubling to me is this: why should students be sharing their answers with other students and critiquing other students' work? Students are to justify their conclusions, communicate them to others, and respond to the arguments of others.
- I pity the shy child who doesn't care to share his/her answers, prefers to work independently and shuns group projects in favor of individual effort.
- I pity the child who does not have the language ability to convey his/her thoughts to others and panics at the thought of expressing his/her work verbally.
- I pity the child who struggles with math taught in this manner and his/her work is shared with other students for their responses.
What is the reasoning for these process lessons and collaboration in math? Maybe this creates the framework in which to integrate the issue of bullying into the math standards when the slower child doesn't participate or gets the wrong answer. Bingo! The teacher can cover her bullying lesson in the language standards for the day with the Math lesson and the teacher can mark it off her list of mandated lessons. The teacher can craft the following problem to address the math facts AND the language arts standard about bullying. Then the class can dissect the reasons children bully other children and integrate language arts in math class. It's a standard writer's dream:
Little Johnny has 14 apples. The bully takes away 6 apples. How many does Little Johnny have left?
Meanwhile, the students and teacher may or may not catch the answer to 6 = 14 - __ is NOT 9.