Social and psychological math challenges

Many students struggle with math, but there isn't a single solution to the problem. As we saw in the last post there are multiple ways to solving 95 * 95. Some great suggestions that were provided by readers:

1) HannahCitizenKane suggested to simplify the problem to one that is easier to solve; Subtracting (95 * 10)/ 2 from the product of 95 * 100.

2) Alexander suggested utilizing a square root property for numbers that add in five, similar to the post on Squares ending with five

3) Maria Miller suggested setting up the problem so that it can be solved using the FOIL (First, Outer, Inner and Last) method.

Two other methods that can be used are: 

• Numbers near 100 
• Tens are mirrors and ones sum to zero 
• Similar, but more broadly applied than the squares ending in five method

Just as there isn't one solution to solving 95 * 95 there isn't one solution in helping students with math. As the problems get more complex students need to enhance and upgrade their problem solving tools, while still utilizing the fundamental principles that worked earlier. If there are flaws in the foundational skills then there will be struggles with the more complex problem solving tools.

An important and potentially foundational aspect of why students might struggle with math is the social and psychological challenges. Some examples are:

• Math is hard / I'm not good at math 
• Math is uncool and boring / I don't want to stand out for knowing the right answer or for liking math
• Math isn't used in the real world / I am only being taught this math lesson so I can pass a test
• Most people aren't good at math / Nobody expects me to be good at math, especially if I'm a girl

What do you think are some other social and psychological challenges related to math? Any solutions that you might suggest?

How do I love thee? Let me count the ways... of solving 95 * 95

The famous quote can be borrowed on this Valentine's Day to look at the beauty of math. In life there are few problems that can only be solved one way, even though only one option may appear to us at first. It takes creativity to see potential solutions that are not obvious. If I am hiking and need water there are several potential options available besides for a body of water. Depending on your environment some creative options for getting water are cutting a green bamboo tree, melting non-salted snow or collecting morning dew with a cloth.

We can creative in solving math problems. Below are four different approaches to solving 10 * 11:
1) Add 10 to the product of 10^2
2) Use the multiply by 11 method
3) Subtract 11 from the product of 11^2
4) Double the product of 5 * 11

How many ways can we solve 95 * 95?
Reply back with how many, and which ways, you would solve the problem 95 * 95.

Multiplying Numbers Near 100

For numbers close to 100 we can utilize this method to quickly calculate the product. 

We will write our example problem vertically and solve our answer working left to right :

   96  

 * 94  

 -----

Step 1) Subtract each number from 100 and write the difference to the right of the number

            1A) 100 – 96 = 4

            1B) 100 – 94 = 6

    96    4

 *  94    6

 ----------

Step 2) Subtract the top number in the example (96) by the result of 1B (6).

96 - 6 = 90

Note you can also do the reverse, subtracting the bottom number in the example (94) by the result in 1A (4) such that 94 - 4 = 90  

The difference represents the two far left digits in the answer

                       96    4

                    *  94    6

                   ----------

Answer:       9 0  _  _

Step 3) Multiply the results of Steps 1A (4) and 1B (6)

4 * 6 = 24

The product represents the two far right digits in the answer

                       96    4

                    *  94    6

                   ----------

Answer:       9 0 2 4