Read on Twitter
Here's some more info about the strategies people in our study (1000 adults) used for this math problem! [thread]
First I'll tell you the strategy codes we used. Note, this is not exhaustive and is just what we came up with - it's not perfect or detailed, just broad categories. https://twitter.com/saraannhart/status/1282740708613521408
First I'll tell you the strategy codes we used. Note, this is not exhaustive and is just what we came up with - it's not perfect or detailed, just broad categories. https://twitter.com/saraannhart/status/1282740708613521408
1) US standard algorithm: What many of us were taught. For example, “I added 5 + 8 = 13, then carried the 1. Then I added 2 + 3 = 5 plus the carried 1 is 6, then I added 1 + 2 = 3, so 363”
42% of responses were coded into this category.
42% of responses were coded into this category.
2) Decomposition by place value: The numbers are decomposed or broken up based on place value and then put back together. For example, “I did 100 + 200 = 300, then 20 + 30 = 50 and then 5 + 8 = 13 and then added those so I got 363”
12% of responses
12% of responses
3) Decomposition in another way: Numbers are again broken apart, but not just based on place value. For example, “I added 125 and 200 to get 325 and then added 38 to get 363”
19% of responses
19% of responses
4) Other: Anything where it was clear what they did, but it wasn't strategies 1, 2, or 3. A number of these involved compensation (adding more and then subtracting). For example, "I added 125 + 250 and then subtracted 12" or "200 + 100. Then 30 + 40 - 7 = 363"
2% of responses
2% of responses
5) Cheating: They said they wrote it down or used a calculator. (1%)
6) Too vague to code: They wrote something, but it was impossible to put it into a category. For example, "I added up the numbers" or "I did it in my head" (22%)
7) No response: They didn't write anything (2%)
6) Too vague to code: They wrote something, but it was impossible to put it into a category. For example, "I added up the numbers" or "I did it in my head" (22%)
7) No response: They didn't write anything (2%)
We haven't done a 2nd pass through the vague ones to see if we can categorize them, so % could change.
Also, within the decomposition and other categories (2-4) there are TONS of different ways people do the problems. It's amazing. You can see it in the quoted thread as well.
Also, within the decomposition and other categories (2-4) there are TONS of different ways people do the problems. It's amazing. You can see it in the quoted thread as well.
So, lots of adults do decomposition or other strategies in their head! Even though most of them were probably not directly TAUGHT how to use these strategies.
Now we do (usually) introduce these to kids in school...since they may already be thinking these ways anyway!
Now we do (usually) introduce these to kids in school...since they may already be thinking these ways anyway!
Also some of these make NO sense to other people. Like, I would NEVER do the algorithm in my head, I get lost in the carrying. The compensation ones too. For me, I'm usually one of the decomposition categories. But, it changes depending on the nature of the problem too!
Okay - so does strategy use relate to anything else? Let me show you a few things...
(These are all quick figures I made, so don't judge (no error bars, etc.). I removed nonresponders. I will not focus much on the cheating and vague groups, but they are sorta interesting.)
(These are all quick figures I made, so don't judge (no error bars, etc.). I removed nonresponders. I will not focus much on the cheating and vague groups, but they are sorta interesting.)
Sex: 53% of females vs. 31% of males used the standard algorithm (red)! I hadn't looked at this before, but...wow that's a big difference.
(you may need to click the figure to see the strategy labels...but they are rainbow order in the order I talked about them)
(you may need to click the figure to see the strategy labels...but they are rainbow order in the order I talked about them)
Math Anxiety: Those using decomposition by place value had lower math anxiety, on average, than all categories except Other. (measure: Hopko MARS-R scale)
Math Fluency: Those using decomposition by other had higher math fluency than those using the standard algorithm. No other differences.
Probability Skills: We gave the Berlin Numeracy Test (Cokely et al.). It puts people into 4 categories, with 1 (red) being lower and 4 (green) being higher. Those using decomposition strategies (either type) tended to have higher scores than those using the standard algorithm.
That's all I've got for now...just some first glances. A few things:
- Most people got this math problem right - so all the strategies work, there is no "right" strategy.
- Some strategies are a bit more likely to be used by certain people or people with certain skills.
- Most people got this math problem right - so all the strategies work, there is no "right" strategy.
- Some strategies are a bit more likely to be used by certain people or people with certain skills.
- Math anxiety and fluency differences aren't big; gender and probability skills diffs are larger.
- It's ok if you use a strategy that seems crazy!
- You can give 1000 people a math problem, and you will get back A LOT of strategies.
- Playing with numbers is really fun!
- It's ok if you use a strategy that seems crazy!
- You can give 1000 people a math problem, and you will get back A LOT of strategies.
- Playing with numbers is really fun!
Also wanted to add - these data are from the dataset @saraannhart and I use in this paper: https://jnc.psychopen.eu/article/view/195/html
And if you are interested in exploring more in the dataset, we have this fun shiny app that @aedwards1010 made with the data: https://idcdlab.shinyapps.io/hart_and_ganley/
And if you are interested in exploring more in the dataset, we have this fun shiny app that @aedwards1010 made with the data: https://idcdlab.shinyapps.io/hart_and_ganley/
