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| 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:
9−3=□8+□=1516−□=5
□=7−213=□+76=14−□
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."
Solution:
Solution
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=6
We 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=15
We 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=5
We 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=7−2
We 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+7
We 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=14−9
We have found the missing numbers in each of the given equations.
Comments
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mboudwin wrote this comment 5 months ago
Would it be beneficial to state in the commentary that the sum could appear on the left side of the equation with the addends on the right to reinforce Standard 1.OA.7?
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BanjoBen wrote this reply 5 months ago
I think that's a good idea. I'll try to see about getting some examples like that added.
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BanjoBen wrote this reply 5 months ago
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.
Did you post a comment at Illustrative Mathematics (not an assessment company)? The spirit of crowd-sourcing resources with the ability to comment and critique is the promise of that initiative. I hope you post there and help provide the feedback necessary to improve it.
ReplyDeleteAs for asking students to justify their conclusions, communicate them to others, and respond to the arguments of others--it is a practice standard worth working with in the classroom. As you note, the problem is not with the standard it is with classroom environments that allow students to learn from each other in positive ways. How can we be creative about this important, relevant practice and recognize the different dispositions of our students? I hope teachers do not embody this standard in this spirit or in this way, but rather find practical ways to do it in a meaningful and beneficial manner.
Mr. B
ReplyDeleteThanks for your comments. One issue I didn't raise is that the teacher's evaluation will be based at a high percentage on HOW the students answer the question. If the answer is not complete enough, the student is rated lower via a point method (even if the answer is correct) if the processes were not explained well. The teacher's evaluation will reflect that as well.
From talking to teachers, many of them are despairing of real teaching occurring vs following the construct before them. I wouldn't agree there is nothing wrong with the standards.
If the standards include deducting points because all the processes were not followed and explained to the assessment's satisfaction (not the teacher's), then the standards are faulty and should be shelved. But as this is impossible because of the CCSS mandates, this practice has to continue in the classroom until parents and teachers finally refuse to have children adhere to a consortia's idea of how to teach math.
This "one size fits all" assessment program is doomed to fail on many levels IMO...because there is not a "one size fits all" human being.
Thanks for pointing out this typo. It was corrected within 11 minutes, as you can see by going to http://illustrativemathematics.org/illustrations/4. I agree such an error would not be acceptable on a high stakes assessment. Illustrative Mathematics is not an assessment company. The purpose of Illustrative Mathematics is to provide tasks illustrating the meaning of the standards. We try to avoid publishing errors, but errors do creep in, as they are bound to in any published materials. It is important to have a process for correcting errors after publication, and we are grateful to the community of users who point out errors or other infelicities in the tasks.
ReplyDeleteI'm still wondering "How much money are taxpayers on the hook for these new math standards?"
ReplyDeleteAre Missouri residents aware that their locally elected school board members have no control over these standards. Check out the states' memomandum of agreement signed by the Governor and the State BoE (bypassing your elected representatives at every turn)
Lisa Jones