We all know how this goes in the classroom when we say “Can you tell me how you solved that problem.” Students often say “I just ‘THUNK’ it in my brain” or “Don’t you know why I knew the answer? It was because I am SO SMART!”Sometimes it is difficult for us, as teachers, to know how to get more quality responses out of our students and to get them to explain their mathematical thinking while using the 8 Standards for Mathematical Practice.

At Strategic Intervention Solutions we work with thousands of teachers each year in mathematics to help them make what we call the “shift” in math. We all know teaching 21st century math is very different than the way we learned and we, as teachers, deserve to be giving time to make this “shift”. We first need to start to help students gain an understanding for how to verbally explain their thinking in math before we can expect them to write about it.

Check out this past blog entry to learn how to get math discourse and number talks into your classroom routinely: https://sis4teachers.org/2014/01/math-talk/

### 8 Mathematical Practice Standard #3:

### Construct Viable Arguments and Critique the Reasoning of Others

Today we want to feature how Communicating Mathematical Thinking can look in writing through daily math journals! These samples are from a very impressive 2nd grade teacher that we work with in Trenton Public Schools in Michigan (this school district is a part of our Systemic Math Initiative & Coaching Project). Journaling is presented in a way for her students to understand that problems can be solved in different ways and they can **Critique the Reasoning of Others** to prove their mathematical thinking. Each student in her classroom has a “Learning Partner” in which they trade math journals with, to provide feedback on their thinking. The students know if they want to comment on their learning partner’s thinking they have to write in a different color to differentiate each partner’s comments.

**SAMPLE #1:**

“I got the same answer as you, but I solved it different….”

**SAMPLE #2: **

“I disagree the results because…”

**SAMPLE #3**

Here she is using our journal template** **and they are using NAPE language (novice, apprentice, practitioner and expert) in their rating of the students math work. LOVE THE COMMENTS IN THIS ONE 🙂

**SAMPLE #4 **

Look at how the students are using the mathematical language in their writing “bonded” “friendly decade number”

WOW right!! So exciting to see the growth of our teacher within our project! Remember to take time first to get students to explain their math thinking orally before moving to writing. Have high expectations for students to use the appropriate mathematical vocabulary within their speaking and writing! We promise that if you start with just 10 mins a day to get student to use this standard you will see a HUGE difference in your students. Who knows your student may come up with a way to solve a problem that you may have never thought of!

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