You have probably heard of the “3 Reads” Math Language Routine. If you haven’t, check it out. One thing it does really well is to help students actually read and contextualize a math problem, before just solving it.

We didn’t measure this by implementing 3 reads in a classroom and measuring their results. Although, we can help with that too! Instead, we asked 9,833 students to explain their reasoning and then measured which of them used 3 reads, or something similar, to help solve the problem.

From there, we looked at the difference between those students and others. Wow, it made such a huge difference! Let’s dive into the details.

This is the question we asked:

The top student answers were as follows:

Student Answer | % of Students |

16 | 50% |

20 | 4% |

19 | 3% |

17 | 3% |

15 | 3% |

Quickly, you may notice that there are going to be a lot of different answers for this question given that the top 5 answers only represent 63% of all the students.

We also saw a lot of nuance in students’ thinking based off their explanations.

“

Student who answered “16”We already know that Steven has 140 in his bank account, and the laptop is $860. So we have to subtract 140 from 860. That leaves 720. I then divided 720/45 to get 16. So Steven has to work 16 days to buy the laptop“

Student who answered “15”

“I figured it out by taking 140 and adding 45 to it then I got 185 then I added 45 to 185 15 times and I figured since it took 15 times to get to $860 then he would have to work 15 days.“

“

Student who answered “20”I figured out how much Steven has to work because I multiplied 45×19= 855, which is not enough for the laptop, so then I multiplied 45×20=900, which is more than enough for the laptop, so he was to work for 20 days.“

We then analyze all of these responses in a detailed way to really understand how students are thinking. We are looking to understand what tools they are selecting to solve the problem (like division, counting, multiplication, etc) as well as how they talk about solving the problem. This can be incredibly useful for identifying the best way to help a student and it can also go a long way towards creating a better culture of explaining your answers in your school.

In this post, we are going to focus on the students who talked about the quantities and their context (as the 3 reads helps students to do).

One quick thing to notice is that students who answer “20” are missing a quantity completely, 140. 140 is in this question is the amount of money that Steven has in the bank. The students who answer 20 don’t use that amount very much. So, I imagine that if we were to look at students who wrote every quantity down, they wouldn’t get 20. Before we find out though, let’s get on the same page about how we can measure if students use the strategy or not.

Part of the three reads strategy is taking the quantities out of the question and giving them context. Let’s do it together.

Quantity | Meaning in Context |

860 | How much the laptop that Steven wants costs in dollars |

140 | How much money Steven already has in his bank account. |

45 | The amount of money Steven can make per day |

So with that, we had our team of math analysts look at almost ten thousand student responses to find which responses had this information and which didn’t.

For example, I bolded the quantities with meaning in context for the following student response:

*“I took the price of the laptop(860). Then removed the amount of money that Steven currently has in his bank account (140). Which equals 720. Then I divided 720 by the amount that Steven makes in a day. Which is 45. 720/45 = 16.”*

Not all responses have all 3 quantities, so we looked for each quantity and meaning in context separately.

What do you think the shift in top 5 answers looks like when we look for these quantities in context?

Student Answer | % of Students | % of Students _{(and has 860 in context)} | % of Students _{(and has 140 in context)} | % of Students _{(and has 45 in context)} | % of Students _{(and has all 3 in context)} |

16 | 50% | 68% | 69% | 61% | 79% |

20 | 4% | 3% | 1% | 4% | 1% |

19 | 3% | 4% | 1% | 4% | 1% |

17 | 3% | 3% | 4% | 4% | 3% |

15 | 3% | 3% | 3% | 3% | 3% |

Wow! First off, just including any of the quantities with meaning in context really skyrockets the percent chance that a student will get the question correct. And if they did all 3, it was an even bigger change. And it doesn’t end there, students who used this also performed much better on the assessment overall **and** on the state test.

As you can see, there is a lot of evidence that the *3 Reads Math Language Routine* can really benefit students.

This is just one of many great routines you can implement in a classroom. At Math ANEX, we work hard to understand how your students are thinking, identify the best way to help them, and help you implement the practices that will best help your students. **Subscribe below to stay up to date with our explorations into students’ mathematical thinking.**