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Students were given 2 problems to work on using the FAST DRAW strategy. The first problem was done in small group collaboration then reviewed as a whole class and the second problem was used as an exit ticket (done independently).

Second problem reads:

The diameter of Mars is 6.8 x 10³ kilometers. The diameter of Earth is about 1.2763 x 10⁴ km. Find how much greater is Earth's diameter than the diameter of Mars?

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Student does not participate during class. When called on, they just say, "I don't know." But, when working with student 1-on-1 or in small groups, they are more willing to take risks.

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Student participates during lessons and gives it a go, even if they are not sure of answers.

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Student actively participates during lessons. Usually, this student needs 1-on-1 explanations / refreshers before starting independent assignments, but they are good to go after a few minutes.

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Integrating FAST DRAW strategy

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Students were given 3 problems to practice the KNOWS strategy. The first problem was a whole-class discussion, second one was small group, and the least problem was supposed to be exit ticket but we ran out of time.

Second problem reads:

Hunter and his cousin Peter wants to build a large square flower garden. They are told the biggest they can go is 121 ft².Hunter finds 4 12ft long planks of wood and says there is enough wood to build a 121 ft² garden area. Peter says it is not enough. Who is correct? Show work and explain your answer.

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Students have difficulty remembering squares and roots

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Whole Class practice of differentiating between Rational and Irrational numbers

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Student's behavior has progressively gotten worse this semester making learning (and teaching) tough, even in isolated 1-on-1 settings.

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Student actively participates in class and gives correctly answers about 80% of the time, but struggles vastly to independently elaborate on his answers using correct academic terms.

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Student is a newcomer and is fantastic in math. They do require time during class for 1-on-1 explanations, but once it's given, they are able to work out problems and get the correct answers.

We are working on elaborations and they are encouraged to say it in Spanish if unable to find the correct words in English. I or homeroom teacher would say it back in English for the student.

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Students demonstrate difficulty independently explaining (verbal and writing) their mathematical reasoning while using academic vocabulary.

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Unless detailed language patterns are provided for each activity, students are unable to confidently explain their reasoning as to how they got their answers.

Even when they get the correct answer and I see the work shown correctly on their paper, they are unable to tell me how they got there.

In addition, when asked to go back and reference their notes, they skim back multiple pages although the topic was just taught that day or recently.

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Students would be able to explain their answers with less guidance/prompt and use academic vocabulary terms correctly. (And with confidence!).

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How can I use structured discourse and instructional strategies with my 8th-grade students to improve their ability to independently explain their mathematical reasoning using academic vocabulary?

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Professional Goal Growth and Measurable Outcome

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Professional Goal Growth and Measurable Outcome

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By the end of this inquiry, I hope to have added at least 2 solid strategies to my repertoire for implementing instructional strategies to help support middle school students in independently explaining their mathematical reasoning (verbally and in writing).

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Students were given a pre-assessment before the start of the unit. The pre-assessment was 10 questions long, with multiple choice, true or false, and. I will be using their raw scores (#/10) for the data collection. All questions are weighted the same.

There are no questions that students would be able to earn partial credit.

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Spring 2026 Academic Achievement Data  - My Data

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When I shared my dilemma and focus question to my principal, Ms. Ripley, and she gave me some suggestions for next steps:

Contact Mr. Vuthy Tim at Lorbeer to ask for tips and possibly observe.

She states he does a fantastic job at getting students in expanding and explaining their reasoning

Observe an AVID class when they work on tutorials

Ripley says that the AVID teachers and tutors do a great job in guiding students with doing tutorials. Tutorials provoke higher-level thinking in small group settings and is student-led

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Mild/Mod Assignment

Suggestions:

Graphic organizers, especially when introducing new concepts

Have to try out different kinds to see what works with the students and topic at hand

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Colleague – AVID Coordinator

What did I learn:

Small group collaborative strategy that promotes student discussion and critical thinking

Focus student shares a "Point of Confusion" and discusses the steps they took to solve the problem and share steps they have taken to try to understand the problem

Strategy places emphasis in academic dialogue and understanding rather than receiving direct answers

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Veteran Teacher – CER

What did I learn:

Prioritize vocabulary in three ways: visually (wall and notes), verbally, and in writing

Use KWL charts to create a visual brainstorm to organize thoughts before writing responses

Most effective strategy w/ CER: Use it as a whole-class discussion using student samples of both “strong” and “needs improvement” examples so students can see what high-quality reasoning looks like

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Online Resource – FAST DRAW

What did I learn:

Helps students become more familiar with different components of a word problem

Encourages structured mathematical discussion

As students verbalize their thinking, they can clarify before transitioning to written explanations

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Online Resource – K.N.O.W.S.

What did I learn:

Structured problem-solving framework designed to support students in analyzing and solving word problems

Promotes clarity and can help improve cognitive thinking when approaching multi-step word problems

Graphic organizer, but can wean students off that support as they internalize the structure and thinking process

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Things to note:

Every student improved

4 students met goal (+6 from original score)

5 students missed the goal by 1 point

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Only a handful of students met the goal I had set (+6 from original score), but every student at the very least improved. The average for the pre-inquiry assessment was 1.6 and the post-inquiry average was 5.35.

I think that the students scored as they did because I implemented at least one of the strategies each week. Sometimes it was twice a week. Students became more familiar with what to do and how to do it.

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Jefferson was one of my students that made the least amount of improvement pre- to post-inquiry. He started off with a score of 1 and ended the inquiry with a score of 3. His goal was to reach 7.

I believe that the student’s behavior throughout this whole inquiry hindered his chance of greater improvement. Instead of teaching him strategies to explain mathematical reasoning, I felt as if I was teaching him more behavior management instead.

Because he is heading off to high school, I would like to focus on him more in hopes that he will be able to internalize the strategies by the end of the school year. I will have to try moving his seat around to see where he focuses best.

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Jacqueline is one of the 4 students that met the goal I set for them.

This student is bright and is always willing to try out different strategies in order to understand what she is learning. She is one of the few students who actively reaches out during independent work time and asks for assistance/guidance if she is confused or lost. And then when she gets it, she gets it. She would, on her own, help out her peers at her table, going step-by-step on how to solve the problem using the strategy that was taught.

She does need some more weaning off when writing mathematical reasonings, but I believe she can get there by the end of the school year.

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Johan is one of the newcomers in the class. He can get by with English, but is definitely much more comfortable speaking Spanish instead. During We-Dos, if he raises his hand and wants to share an answer, I let him do so in Spanish and ask afterwards if he can try to say it in English too.

I was worried about Johan’s progress in the class, as was gone for a few weeks at the beginning of the semester and continued having spotty attendance. When he would be gone for however long, I or the classroom teacher would have to work overtime to try out best to catch him up. But despite language barriers and attendance issues, he is brilliant at math.

It takes him a bit to get the lesson, but once he gets it, he goes off on his own (occasionally calls me back to check his answers). If he works on his attendance

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For my current students, I would like to continue practicing these strategies and eventually have them lead whole-class discussions. They are having lively discussions in small groups, but this does not yet fully transfer to whole-class discussions. To support this transition, I will continue to incorporate topic-specific sentence stems to help students explain their reasoning and critique the thinking of others.

I will also use structured routines such as think–pair–share to gradually build confidence in sharing ideas publicly.

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Thoroughly teach and practice the strategies at the beginning of the school year for future students. That way, students have a plethora of tools they can reach during their FIABs, PSAT, and other formal (and informal) assessments they have to do.

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Using the strategies that I researched and implemented in this inquiry helped me structure both whole-class and small-group math discussions. I was able to see more clearly where my students needed additional support, which helped me determine target students to focus on during independent work time to provide extra guidance and implement these strategies one-on-one.

I can also see and hear my students’ confidence growing when I ask them to elaborate on their answers. I hear fewer “I don’t know” responses during the period and receive less incomplete work.