• Plan before the number talk. Planning for connections and anticipating students' strategies. Thinking about what students will offer will help the teacher explicitly identify the strategy and share vocabulary with the students so that they will use the math terms when explaining their strategy.

• Knowing the difference between strategies and representations. A strategy is how to deal with numbers or the structures to solve the problem; where representations are the models of strategies to use to build relationships. Misusing these terms can develop misconceptions among the students. So, it is important to be clear during number talks and pay attention to how students talk about strategies and representations to point out if it is a tool they are using or structure.

• Be intentional and explicit. Think about the problem that you want students to solve, think about the next day, and how that could follow. Teachers have 10 minutes in their day to incorporate a class discussion surrounding math.

Question 5:

• They expressed teachers should use the same strategy the whole way through. I thought number talks allow students to see different representations/ explanations, so should teachers use the same strategy?

• Another question I have is if a student is lost during a number talk, how should the teacher approach the situation knowing that you want to keep the number talk short?

TM

• Math teachers should also focus on reducing the stress of their students and including mindfulness activities and time for reflection along with instruction. If students are feeling stressed, they will lose motivation. 

• Be mindful of students’ cultures when presenting math problems. We often ask about holidays, measurements, sports, or food in story problems that students who are new to the country may not be familiar with. We need to find ways to make this easier on our newcomer students without “dumbing down” the math. 

• Newcomer students may have a knowledge of math, but not a knowledge of math language. Traditional assessments may not be an effective or equitable way to measure the knowledge of newcomer students. We must think about all of our actions and ways in which we can position our newcomer students to be successful. 

Question 5:

• Have you ever experienced, either as a student or in field experience, a teacher presenting math problems in a way that was not equitable to all students? How did this make you/ the students feel?

• Could you see yourself implementing these practices in your future classroom? What are some other ways to teach mathematics equitably?

LVD

• The first thing the presenter hopes is for you as the teacher to talk less to the students, to entice them to want to talk more and it even helps them to understand more. When students are given the opportunity to talk about their thinking and to share with others about their thinking they are deemed to be more successful which is what we want.

• The presenter also wants us to teach resilience during math because that is one area that needs it the most. She talks about helping to improve our student’s character and we can do that through math. She thinks that if we incorporate resilience into our math time we can increase the understanding in our students.

• The last major thing the presenter wants teachers to be mindful of is steering away from controlling the discussion to facilitating the conversation. It's all about amplifying our student’s voices. We value our students and we should give them the opportunity to share their thoughts. 

Question 5

• If you have an older grade (3-5), what are ways you are planning to get them excited for math? Will you have them lead discussions?

• How can you as a teacher empower your students when it comes to difficult math concepts? 

EG

Overarching Concept: Productive struggle

1. Tasks: Teachers should provide opportunities for students to productively struggle and work through problems that they have not been told how to do. However, teachers must be sure that students are feeling challenged rather than frustrated. McMorrow explains how mimicking is less effective and is not learning or thinking. To implement tasks teachers should develop 4-6 non-curricular tasks before doing any curricular task. These non-curricular tasks help students feel safe and also help students feel it is acceptable to be stuck. These also don’t require much content knowledge. This will help students gain confidence and prior knowledge before starting on curricular tasks.

2. Visibly Random Groups: Teachers should implement visibly random groups to ensure an equitable learning environment. To implement this, teachers should create new and random groups. Groups of 2 for grades kindergarten through 2nd and groups of 3 for third grade and up. This helps increase student engagement, eliminates social barriers, increases the mobility of knowledge between students, and increases enthusiasm for the topic. However, teachers must create an efficient way to provide random grouping. This could be done by passing out matching cards and then students have to find their partners.

3. Vertical Non-Permanent Surfaces: Teachers should have their students use vertical non-permanent surfaces. To implement this, teachers should use one marker and one vertical whiteboard. This helps create opportunities for knowledge mobility. This is because students are more likely to take risks and make educated guesses as it’s not a permanent surface. This also increases eagerness to participate.

Question 5:

1. Why do you think mimicking is less effective than productive struggle tasks?

2. Thinking of your own educational experiences, how might the incorporation of productive struggle have impacted your experience in school? As a student, would you have preferred this way of learning math?

K.O.

• New ways to assess students:

  • Older ways to assess multiplication are not effective, an example of this is mad minutes, where students have a minute to show what they know. A new way to assess students' multiplication skills is presenting them with five different math facts, have them solve the facts, and then ask the student if they automatically knew the problem, or used a strategy to solve it.

• Building Mathematical Reasoning:

  • Mathematical reasoning is applying logical reasoning to math problems. An example of this is a student is given a math problem 6x7, they solve it by multiplying 5x7 and adding another 7. This shows that the student has an understanding of multiplication, and not just knows it from memory.

• Extension:

  • This is for students who already know their math facts and need a challenge. Multiplication facts may be learned, but the learning is not done. Present students with more complex multiplication problems where they have to use prior knowledge to solve.

    
    

Question 5:

1. In my field experience, a lot of students do not know their multiplication facts. How can you encourage the learning of multiplication, but continue with fifth grade math standards that have moved on from multiplication?

2. Do you have any ways you can assess students' multiplication knowledge without using timed tests?

JH

• How did your expectations of teaching math change after watching your video? 

• What do you plan to do differently going forward as a teacher during lessons?

KG

They also hope to bring in group work as much as possible for students to build and bounce ideas off of each other.

VNPS Vertical non permanent surfaces make for a great change in our math thinking.

5. Do you think it is important to get a change of how we work on our problems?

Why do you think it is important to have different sized groups depending on the grade?

MD

• anticipate student thinking for multiplication and division

• observe and describe student thinking 

• understand learning progressions and learning trajectories 

• make connections for planning intervention

• In my field experience, students struggle with using models, they would rather just do the problems in their head. How do you make sure students show their work and their process of getting the answer?

• Some students in the group had a hard time understanding multiples of 8 but are working on division problems. Shouldn't they take a step back?

KM

• Active Questioning and Problem Posing: Nolan describes how as educators we should prioritize developing skills in questioning techniques and problem-posing strategies to assess student understanding effectively.

• Utilization of Visual Aids and Manipulatives: The presenter helps us understand the importance of incorporatong tools like the Fraction Kit to enhance conceptual understanding and promote active engagement in problem-solving activities.

• Promotion of Critical Thinking and Student-Centered Learning: Ed Nolan states that designing activities that encourage critical thinking, collaboration, and student ownership of learning to foster deeper understanding in mathematics.

Q5-

• TQE Process for Task Selection and Questioning: Introduces TQE (Task, Question, Evidence) as a framework for task selection, questioning, and assessing learning.

• Promotion of Critical Thinking and Student Engagement: Emphasizes fostering critical thinking and active student participation in knowledge creation.

• Teacher's Role in Planning and Reacting to Student Thinking: Highlights the teacher's crucial role in lesson planning, responding to student thinking, and using tools like the Fraction Kit.

  
  

Continued Q5 (benefits of key elements for young math learners)-

• TQE Process for Engaging Learners: Guides students through tasks, questioning, and assessment to foster critical thinking, problem-solving, and varied demonstrations of understanding.

• Promoting Critical Thinking and Engagement: Encourages exploration beyond memorization, fostering curiosity, creativity, and deeper comprehension for practical application.

• Teacher's Role in Creating Supportive Learning Environments: Effective planning, responsive teaching, and use of tools like the Fraction Kit cultivate confidence, motivation, and a growth mindset, making math concepts more tangible and accessible for young learners.

RD