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The presentation gives five questions to use when determining what to implement: Is the experience designed with kids, so I know it’s meaningful and authentic to them? Is the investment of time/energy worthwhile for me and my students? Is the impact of student learning proportionate to the class time expenditure? Is there a sustainable approach to creating time in our schedule for this? These questions are for educators to use when filtering new strategies, activities, and ideas to decide what is best for their classroom and for them so that they do not become overwhelmed with what they take on.

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Katelynne - Number Lines Across the Curriculum (PreK-5) by Kara Rihn

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Katelynne - Number Lines Across the Curriculum (PreK-5) by Kara Rihn

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Q4 - One thing the presenter hopes teachers would do in the future is help students recognize zero on a number line. Many students go into second grade and not understand the concept that zero is a starting point on the number line. This is ultimately something a teacher must emphasize. Another thing the presenter hopes teachers will start doing more is to use websites such as brainingcamp to help students build a good foundation for numbers. The tools on this website are visual which helps. students see what exactly is going on in a math problem. The last thing that the presenter hopes teachers would incorporate into their math lesson is an open number line. This challenges the students understanding of numbers and is a good way to assess the students to see if they get the concept.

Q5 -
1. What was your experience like with number lines in school?

2. What manipulatives, other than a number line, would you use to help your students make sense of numbers?

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"What is the essential element of the task that must be preserved"
"What aspects of the task might make it inaccessible to the student"
"What presentation modifications can I make to lend accessibility and yet preserve the intent of the task?"
"What supports are needed to enable the students to demonstrate their content mastery?"
"Are the students able to generate a response independently or will it be helpful to provide choices"
"How will we use this information to build knowledge"

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Hayley Patock: Don’t Unwrap the Present for Your Students (PreK-5) with Nicole Thompson & Jessica Batinovic

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Hayley Patock: Don’t Unwrap the Present for Your Students (PreK-5) with Nicole Thompson & Jessica Batinovic

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The presenters had three main guiding principles they discussed: students need to be able to understand math, teachers carefully guide students in meaningful material, and teachers need to have the knowledge themself. They believe students need to experience productive struggle, where the material is not too easy and not too hard. This is beneficial because students are able to work together to come up with answers and think deeply. This allows students to be able to make mistakes, and learn from them. They also believe in the rapid release model, where students explore the material before the teacher actually teaches it. This would be a classroom that focuses on "You do, We do, I do" instead of "I do, We do, You do" (gradual release model). The benefit for this is that it gives students the opportunities to collaborate. It also promotes a classroom where students are able to promote their own knowledge. Counting collections was also something the presenters went over. This is where the teacher has the students count a large collection of items. The teacher walks around and observes what techniques the students are using to count, and this also gives the students the opportunity to learn from one another by sharing ideas. Also, when involving story problems in the classroom, it is important the student is invested in the problem. This could be done by giving story problems the students can relate to (candy for Halloween).

Questions:
1. Why do you think it is important for students to be active learners in the classroom? What benefits come from this?

2. What are ways students can have their own AHA moments in the classroom? What approach can teachers do in their teaching for this to be accomplished?

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Macaire Brown = Finding the Foundation for Each and Every Student (PreK-5) By: Dawn Dibley

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Macaire Brown = Finding the Foundation for Each and Every Student (PreK-5) By: Dawn Dibley

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Q4: Right off the bat, the presenter welcomed everyone by listing off different cultures as well as different job titles and more. One thing the presenter hopes teachers would recognize (even herself), is that people with different skin colors experience the world and schooling differently than the teacher might. The teachers need to recognize that students with different abilities and students with different opportunities need to be looked at differently. Another thing the presenter hopes the teacher would do in the future is to observe their students instead of just looking at the assessment they gave that child and defining the student by the results of the assessment. Ask the students questions, see what they do with the problem, and see if they are doing the problem productively or not. The last thing that the presenter, Dawn Dibley expressed in hopes for the teachers to do would be to do subitizing. The ability to subitize dot patterns will give students the ability and experience to determine a certain quantity without having to count by one and see collective individual items as one group. This will set the stage for the actual ability to compose and decompose quantities, and add and subtract without having to keep counting by one.
Q5-
Question 1: What was your relationship with your mathematics teacher like in middle school? Did that teacher make you learn a certain way?
Question 2: Students with learning differences might create some difficulty when you are a teacher and you're trying to assess what they've learned. How do you think you would assess a student with a learning difference?

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Paige Kalantzis: Division that Doesn't Make Students Cry (3rd - 5th) by Pam Harris

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Paige Kalantzis: Division that Doesn't Make Students Cry (3rd - 5th) by Pam Harris

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One thing the Pam Harris wants teachers to incorporate in their classroom is to treat math like a chess game. What she means by this is; math is strategic! When looking at a math problem, treat it like you are looking at a chess board, by analyzing the relationships between each game piece and planning strategies based on these relationships.

She also stresses that we as teachers spend a lot of our time towards making math fun and engaging for our students. This entails raps and songs that reference other people’s ways of thinking, and how to memorize or copy those ways of thinking. Harris calls this making math “cute.”  She wants novice teachers to instead focus on making math engaging through using what we know (accessing prior knowledge) to solve problems – like mathematicians do! There is greater reward in teaching students how to strategize and think using what they already know rather than asking them to memorize the way another person thinks.

The last detail Pam Harris wishes teachers will consider is the development of mathematical reasoning. She shared a graphic that displays mathematical reasoning starts with counting strategies, which helps develop additive reasoning, then multiplicative reasoning, proportional reasoning, and functional reasoning. For students to understand division, they must have their multiplicative reasoning developed. She explains that each level builds upon the next and helps with each stage of math. Harris stresses that math is not necessarily easy, and that it might feel daunting after using a lot of mathematical thinking. However, it should be noted that however daunting it might feel, it is always “figure-outable.”

1.       How do you think this form of mathematical instruction would have impacted your experience in school?

2.       Do you think that memorization can be beneficial in any instance with mathematics?

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Paige Arendt- Fewer Things, Better: Making Time for What Matters Most (PreK-5) by Angela Watson

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Paige Arendt- Fewer Things, Better: Making Time for What Matters Most (PreK-5) by Angela Watson

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Q4-
The presenter wants math teachers to be mindful of how they are spending time in the classroom. She also wants them to think about the professional development and materials they are implementing to ensure that they are meaningful and not going to make things more overwhelming for the teacher. She talks about how teachers sometimes do too much. She claims, “Stop spending hours creating lessons that you’re not going to have time to implement.” Angela Watson wants teachers not to plan for the ideal day because it is not real and instead plan for buffer time and be present in the classroom. These are incredibly useful advice and something I should keep in mind while writing my lessons. Sometimes I pack in so much, but I need to understand that some things might take longer and that is okay.

Questions:

1.     What would be a good rough structure of a math block?

2.     What type of decisions during instruction are math teachers making? Why is it important that they make these decisions?