[BlindMath] middle school math

Thu May 2 23:16:19 UTC 2024

I can empathize with both of you. I have a middle-schooler too, and we sometimes work together on math problems. This has (mostly) gotten easier over time, but we struggled with some subjects when he was younger. In fact, I home-schooled him for a year during the worst of the pandemic because we struggled so much with the online platform his public school provided. This is one reason I was so happy to learn that under the new ADA Title II Final Rule, online course content will be required to be accessible. This doesn't address the issue of handouts or similar materials, and I wish there were a better solution. I am cautiously optimistic that generative AI will lead to advances in this area. 

Angie 

Sent from my iPhone

> On May 2, 2024, at 6:28 PM, Dennis Clark via BlindMath <blindmath at nfbnet.org> wrote:
> 
> Hello John,
> 
> I very much enjoyed your post. My wife and I are both blind and our daughter is sighted and in first grade. We continue to struggle with asking our daughter what is printed on the pages of her math assignments so we can help, but this is difficult to do without causing her to become frustrated with this additional burden being caused by our blindness. She is only 6, and using her energy and concentration to get us synchronized before she begins seems like an unfair position to put her in, and something no student must do whose parents are sighted.
> 
> 
> I noticed you are in California. Are you by chance in the L.A. school system? Most of the schools here are using "Eureka Math" which is apparently some sort of "Singapore Math" variation. I think this is recent and probably was begun after your son started his educational adventure. I look forward to hearing from you if you have a moment.
> 
> Dennis
> 
> 
>> On 5/1/2024 4:12 PM, John via BlindMath wrote:
>> Hello,
>>> I am totally blind and use braille to work out my math problems.
>>> 
>>> For a true K-12 math problem I went to the back of my bedroom closet and brought out my Perkins braille writer.
>>> 
>>> I have a son who is sighted and in middle school.
>>> 
>>> He is good at math and likes it.
>>> 
>>> In a recent math unit he shared with me a math problem he did about area and how he showed his work and how he arrived at the right answer.
>>> 
>>> This was a fun and rewarding family interaction about math.
>>> 
>>> Then he entered a different math unit in the course.
>>> 
>>> The math unit is about proportion, percent, and simple interest.
>>> 
>>> He asked for some guidance from dear old dad to make sure his work was correct and he was learning the concept as intended.
>>> 
>>> If you are wondering what is being taught in common core in the state of California for a typical math class, the order of the concepts is different from what it was in previous years.
>>> 
>>> This particular math unit is about multiple digit multiplication and division. It is actually pretty challenging. For in class exams the student is allowed pencil and paper and no calculator.
>>> 
>>> A solution with a correct numeric answer does not receive full credit. Steps must be provided in writing along the way explaining what is being done and why.
>>> 
>>> A test might have 10 problems and be assigned 45 to 50 minutes for completion.
>>> 
>>> I am so glad I requested extra time as a blind person for all the math classes I ever took.
>>> 
>>> I believe I am hard-pressed today to complete my son's middle school math test in the time allotted for a sighted student.
>>> 
>>> I am not being tested here but I have been asked to add value to my son's learning experience.
>>> 
>>>  
>>>  
>>> First to the fun problem about area. Which is the larger slice of pizza? Is it one eighth of a 16 inch diameter pizza or is it one quarter of a 12 inch diameter pizza? The more I thought about this problem the hungrier I got. Notice that this is very much a multi-step problem.
>>> 
>>> First we write some notes about the problem.
>>> 
>>> diameter d1 = 16 inches
>>> 
>>> portion p1 = one eighth
>>> 
>>> d2 = 12 inches
>>> 
>>> p2 = one fourth
>>> 
>>>  
>>> Solve for area of slice or sector.
>>> 
>>> area a = p times pi times r squared
>>> 
>>> radius r = d divided by 2
>>> 
>>> r1 = 16 / 2 = 8 inches
>>> 
>>> r2 = 12 / 2 = 6 inches
>>> 
>>> slice area a1 = 1 / 8 * pi * 8^2 = 8 pi inches squared
>>> 
>>> slice area a2 = 1 / 4 * pi * 6^2 = 9 pi inches squared
>>> 
>>> So the one fourth of the smaller diameter 12 inch pizza is more area than the one eighth of the larger diameter 16 inch pizza.
>>> 
>>> Grab the slice from the smaller diameter pizza if you want to get full.
>>> 
>>> Who knew?
>>> 
>>>  
>>> Now on to a problem about simple interest.
>>> 
>>> Since I have been seeing the homework problems I will tell you that simple interest is calculated as follows. Let the loan on principle p at interest rate r percent be for y years.
>>> 
>>> The total simple interest in dollars is then p times y times r divided by 100
>>> 
>>> The total amount owed is p plus the simple interest.
>>> 
>>> Here is the simple interest problem statement.
>>> 
>>> A music store sells a bass guitar for a cost of $1800.
>>> 
>>> A student takes a 4 year loan at 15.25 percent per year simple interest. Over the 4 year period how much is each equal monthly payment to pay for the cost of the loan?
>>> 
>>> My interaction with my son on this problem did not go well at all.
>>> 
>>>  
>>> There were some raised voices.
>>> 
>>> We were both pretty frustrated.
>>> 
>>> He read me the problem and I wrote down the wrong problem.
>>> 
>>> I then proceeded to tell him he should get some answer that he should not get.
>>> 
>>> It took us a while to figure out what was going wrong. He could not read my step by step in braille.
>>> 
>>> I could not read his step by step in print.
>>> 
>>> We should not have tried to do this problem ten minutes before bed-time.
>>> 
>>> Math is really not meant to be spoken out loud. Abraham Nemeth has provided some guidance about how to speak math out loud.
>>> 
>>> When there is a fraction that needs to be spoken you have to say begin fraction, speak the numerator, say over, say the denominator, and say end fraction.
>>> 
>>> My son and I had glided through life without practicing this method with each other until we hit this problem.
>>> 
>>> He probably needs to read me the problem, I have to write it down in braille, recite it back to him, get confirmation I have the right problem, and then we can attack the problem together.
>>> 
>>> In an ideal world my sighted son would have an approved 504 plan filed with the school district since he has a blind parent and a copy of his tests and homework assignments would be sent home in hard-copy braille.
>>> 
>>> The blind parent would need some kind of accessible reference material provided as well that teaches the concepts under review.
>>> 
>>> It would be nice if my son and I could spend the time on how to solve the problem rather than what is the problem.
>>> 
>>> Working with a sighted reader who is not my son is one way I could come to the tutoring session with my hard copy braille notes about what the problems are ready to go.
>>> 
>>>  
>>> So how to solve the simple interest problem?
>>> 
>>> Some notes about the problem.
>>> 
>>> principle p = $1800
>>> 
>>> interest rate r = 15.25 percent
>>> 
>>> loan duration y = 4 years
>>> 
>>> Solve for monthly payment m.
>>> 
>>> There are 48 monthly payments in 4 years.
>>> 
>>> simple interest = p times y times r divided by 100
>>> 
>>> simple interest = 4 * 15.25 / 100 * $1800
>>> 
>>> simple interest = 61 over 100 times $1800
>>> 
>>> simple interest = ($1800 over 100) times 61 = $18 times 61
>>> 
>>> simple interest = $610 plus 8 times 60 plus 8
>>> 
>>> simple interest = $610 + $480 + $8 = $610 + $488
>>> 
>>> simple interest = $1098
>>> 
>>> total loan cost c = p plus simple interest = $1800 + $1098 = $2898
>>> 
>>> monthly payment m = c divided by 48 = $2898 divided by 48
>>> 
>>> I cheated and asked Siri what is $2898 divided by 48.
>>> 
>>> You can do long division using a Perkins braille writer.
>>> 
>>> You can do it using an abicus.
>>> 
>>> I got to wondering where is my abicus?
>>> 
>>> I think it is in my top dresser drawer under other stuff.
>>> 
>>> Siri reported the answer $60.375 rounded to the nearest penny is $60.38.
>>> 
>>> Let's check our answer.
>>> 
>>> The answer is about money. You lose a lot of points if the answer does not include the dollar sign.
>>> 
>>> $60.38 times 48 = $2898.24
>>> 
>>> This is close enough to $2898.
>>> 
>>> If total loan payment c is $2898, how much is simple interest?
>>> 
>>> simple interest = $2898 - $1800 = $1098.
>>> 
>>> $1098 divided by 4 = $274.5
>>> 
>>> $274.5 divided by $1800 = r = 0.1525
>>> 
>>> r percent = 15.25
>>> 
>>> Given monthly payment, principle, and total interest paid, the correct interest rate of 15.25 percent can be found.
>>> 
>>> So the double-checked monthly payment is $60.38.
>>> 
>>> On the blind math list serve I do not know how to show $2898 divided by 48.
>>> 
>>> If I did list the steps of the math task I would lose my audience.
>>> 
>>> Working out long division and working out long division with decimals is an important class of math problems for us blind folks to share with each other and to share with our sighted kids.
>>> 
>>> But how to share this information between blind and sighted individuals is not easy.
>>> 
>>> Thank you for reading.
>>> 
>>> very best,
>>> 
>>> John
>>> 
>>>  
>>>  
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> 
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