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8. Elicit and use evidence of student thinking

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8. Elicit and use evidence of student thinking

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The use of a diagnostic interview proves to be very useful when analyzing student thinking.  During a diagnostic interview, the teacher gives a student a math problem to solve.  While solving this problem, the student must show their work as the teacher asks questions in an attempt to better understand the thought process of the student.  I conducted a diagnostic interview with a student to determine if the student was understanding the previously taught lesson on telling time.  Using this information, I could learn what the students are thinking and determine if my lessons are being taught successfully.  I have attached a reflection on this diagnostic interview.

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Assessment of student thinking interview and observation

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7. Support productive struggle in learning mathematics

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7. Support productive struggle in learning mathematics

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The use of productive struggle is important for procedural fluency and understanding.  Students need to work through problems on their own to develop an improved conceptual understanding.  This challenge enhances their ability to remember the concept and strategy for a longer period of time.  I intend on using productive struggle in my future classroom to enhance the learning of every student.  Below, I have attached an article that discusses the importance of productive struggle and introduces an online resource called Waggle.  This website is full of activities and mathematical problems that support productive struggle.

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6. Procedural fluency from conceptual understanding

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6. Procedural fluency from conceptual understanding

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If a student is able to understand a concept well, then they will be able to identify multiple procedures when solving problems.  For example, a student may be able to identify a few ways inwhich they can solve a double digit addition problem.  If they understand the concept of addition well, then they can identify more than one procedure that can be used to solve the addition problem.  Once they are able to identify numerous ways to solve a problem, they will find a method that they prefer.  I have attached an image of a "What's Best and Why?" planning sheet.  This exercise gives students the opportunity to compare two different procedures and determine which one is better.  I intend on giving the students the freedom to solve problems anyway they prefer as a future teacher.  Once they are able to solve a problem in more then one way, then they have an excellent understanding of the concept.

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The use of purposeful questions provides valuable insight on a students understanding of a given concept.  Not only that, but these questions help a student dive deeper into the problem and develop a more thorough understanding.  I have attached a PDF that includes multiple purposeful questions that can be used in any lesson.  This list can be used by any current or future educator to gain an improved understanding of the use of purposeful questions.  I intend on using many of these questions in my future classroom.

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4. Facilitate meaningful mathematical discourse

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4. Facilitate meaningful mathematical discourse

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One way to encourage mathematical discourse is through a number talk.  A number talk is when a teacher leads a mathematical discussion as the students solve problems aloud and share their thinking with their classmates.  I intend on using number talks on a regular basis in my classroom to encourage discourse.  I have attached a lesson plan for a number talk I performed inwhich the students were given data and had to discuss how they would represent it in a table.

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3. Use and connect mathematical representations

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3. Use and connect mathematical representations

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The compare and connect strategy is useful when looking at two different mathematical representations.  The students have the opportunity to look at two different ways inwhich a problem can be solved.  They can identify ways in which the strategies are similar and different.  This strategy is affective because it gives students the opportunity to compare methods they can use to solve a problem.  I would use this strategy in my classroom so that the students are able to identify multiple ways to solve a problem and compare them.  I have attached an image of a planning sheet for a Compare and Connect discussion.

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2. Implement tasks that promote reasoning and problem solving

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2. Implement tasks that promote reasoning and problem solving

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The I-THINK strategy is excellent for students to practice using their reasoning and problem solving skills.  It gives them a chance to break up a problem into multiple steps and think their way through it.  I could promote this strategy when teaching word problems.  The one problem we used to practice this in class was:
"Josh has 20 temporary tattoos.  He plans to give some to Paige and some to Karen. How many tattoos will each person have?"
We then broke it down into I-T-H-I-N-K to solve the problem.
I - Independently think about the problem
T - Tell me what you think this problem is asking you to do.
H - How can you solve the problem?
I - Identify a strategy to use to solve this problem. Use only words.
N - Notice if your on the right track.  Solve the problem using the plan from I.
K - Keep thinking about it. Why is that right?

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1. Establish mathematics goals to focus learning

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1. Establish mathematics goals to focus learning

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Below I have posted the parts of a lesson plan inwhich I aligned my objectives and assessments.  These objectives were used as goals to guide the lesson on one-to-one correspondence.  The use of objectives focused the learning that took place within the lesson. Following the completion of the lesson, I used a checklist to guide my assessment of the students understanding.