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Williams message was that in order to create a successful classroom/community, we need to engage in each other's teachings and ways of learning. We need to consider every child's learning style and accept help/give help when needed.

I have learned that we should always focus on the student as a person and not just as a student. If we work together with the student, they will want to learn better. This is great for math because a lot of students feel they cannot do math and working with them to find ways to help them understand will be beneficial.

The presenter hopes that 1) Teachers will focus more on the student as a person, 2) Help until the student can teach the thing learned, 3) Be patient

1. How could we as teachers receive help if we cannot teach a student a way they can learn best?

2. Should we create a community with the parents directly or through the student?

Williams, Ken. (2022). Better Together. The 2022 Math Virtual Summit. https://www.therecoveringtraditionalist.com/vms-2022/

Dianna LeCrone

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3.  The presenter talks about being able to figure out the denominator first, which is something I remember a classmate mentioning that it is always easiest to find your denominator first. In class we also talked about thinking of fractions in different ways, and the presenter mentions division when working with fractions. I remember doing this in class when we would work with fractions.

4.  The presenter mentions having the students use an interactive website that allows them to play and simulate the lessons they are learning, allowing them to work the problems out themselves. The presenter wants teachers to really spend time on equivalent expressions, and cracking down on numbers. The presenter also wants us to focus on equivalent fractions in decimals as well. Before you move on to operations, equivalent expressions should be worked on even with decimals.

5. Is finding the denominator in fractions easy or hard for you? (take a survey) & Is finding an equivalent to fractions and decimals difficult for you? (take a survey)

Emily G

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2. In, “Reimaging Face-to-Face and Remote Instruction Wills gives tips and tricks with class management and class engagement and interactiveness. After the devastating virus that swept through our Country in 2020, the classroom has changed. With many teachers having to do hybrid learning, and adjust to students being online and in person. Will shows many free activities she has provided to help with the struggles many teachers are still facing right now.
3.Two things I have learned in Dr. Will’s  presentation is how important class community is, and how important it is to know your students and their cultures. Dr. Will used an example, she was starting a lesson on Conics. She had her students take a picture of their favorite food in a bowl. This allowed Dr. Wills to get to see a picture in their house, along with getting to know their student’s culture by seeing what foods they like and eat. Also with younger students, this helped get families involved, and their parents could be a part of their math talks.  In my Education 101 course, my professor emphasizes the phrase, “You cannot teach whom you may not know” . I couldn't really think of ways for teachers, particularly math teachers to get to know their students individually using math. Therefore this is a great example, and I plan to use this concept in my future teaching. Second, Dr. Wills uses Math Talks, similarly to the one stated above. Dr. Wills also uses an example of estimation 180, where students estimate how many objects are on the screen. This gets students very involved, and grows their confidence as there is really no wrong answer. In Math 108, we use Math Talks frequently, and Professor Kaduk mentions the importance of incorporating Math Talks in a classroom setting.
4. Three things Dr. Wills mathematics teachers would start doing or be mindful regarding the idea of first having students take charge in their mathematics. Dr. Wills uses a farm activity for elementary students learning how to add and subtract and learn how to make an equation. Dr. Will had a template where there were farm animals students can move on their screen. Then the students filled out the missing words from the prompt. For example: Student A dragged 4 ducks by the pond, and 4 ducks by the farm house. Therefore student A would fill in the blank that there were 4 ducks by the pond and 4 ducks by the farm house. Lastly student A would then type the equation; 4+4=8. Along with these activities, students are learning technology and how to drag objects on their screen. This is the second thing Dr. Wills wants teachers to start doing and being mindful of. Dr. Wills shows how students must be able to learn technology to be able to be successful in online learning. Therefore activities where they have to drag , and learn how to duplicate or add or take away objects is helping the students improve their skills needed to be successful. Third Dr. Wills wants teachers to be mindful of the classroom community, she states how during online learning she was able to be more involved in her daughter’s class and education. Therefore Dr. Will states the importance of keeping parents involved even in in-person learning.
5. Two Questions: How can I keep elementary students engaged while learning online? How can I have my in-person and online students interact together to create classroom bonds, rather than being two separate groups?

K.O

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2. In, “Communicating Like Mathematics” by Shelby Strong, Strong discusses the importance of discussion in the classroom, and how to hold meaningful and productive discussion to better students' understanding of mathematics. Strong begins her presentation by stating, “Research has indicated that students develop understanding when they are expected to explain and justify their answers.” (Strong, 2022). Strong also uses the concept of math talks to have her audience understand her point of view, by having her audience do math problems that prove what Strong is trying to convey.

3. In Math 108, Professor Kaduk stresses being able to explain and discuss your answer, this connects back to Strong’s message that students need to be able to discuss and explain their answers. Two things that I have identified in Strong’s presentation which is parallel to something that I learned in class is Math talks, and High Ceiling and Low Floor problems. First, Strong implements Math talks into her presentation, the same way as Professor Kaduk implements Math talks into her lectures. Math Talks are a concept where students are able to share and analyze their thinking, along with asking any questions or pose any observations. With many Math Talks with professor Kaduk, and Strong, they incorporate high ceiling low floor problems therefore every student has a chance at attempting the problem, and there is no wrong answer. Therefore students gain confidence in mathematics, and learn how to discuss and explain their reasoning on a problem. An example that Strong used as a high problem, low ceiling problem included a problem where you had to figure out what was different about one of the equations. Strong had provided four equations, and the audience had to figure out which equation was different. However, there ended up being no wrong answer, and the concept of the problem was to get the audience to think and reason what could be the answer, and see how others came up with different reasoning and answers
4.Three things Strong hopes mathematics teachers would start doing or be mindful regarding the idea/phrase , is “stop believing kids are not capable of that”. Strong believes that at no matter level students are at, all students are capable of having essential discussions in mathematics. Second,  while vocabulary in mathematics is important, it is not everything. Strong suggests that it is important for students to understand complex vocabulary in mathematics as students will need to understand that complex vocabulary for standardized tests, or other opportunities. However, Strong suggests that students do not have to first learn concepts with complex vocabulary, but rather introduce those complex vocabulary when they better understand the concept. Strong uses an example of when she asked a student of what they thought a vocabulary term meant after the lesson. The student answered in a simplified answer, but Strong then had a class discussion with all the students to come up with a complex and better understanding of that vocabulary word. Third, allow your students to have wait time when you pose a question to your students. Strong states how allowing a pause when following up for an answer from the students, this allows for a deeper thinking time period, along with students feeling they do not have to rush for an answer, or say the first thing that comes from their mind. Strong states this will allow many students to reduce their anxiety , as they do not feel pressured to answer the question right away.
5. Two Questions: Strong focuses on many examples that are focused on the High School level, how can I alter the examples she provided for Elementary level?

How can I get the more quiet and nervous students to share their answers, and be part of the discussion?

K.O

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PD #3: Alicia Burdess Big Beautiful Problems

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PD #3: Alicia Burdess Big Beautiful Problems

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Alicia went through a variety of problems with the attendees, encouraging them to work together and take different approaches to reach a solution.

The first thing that relates to class concepts is low floor and high ceiling problems. These are a lot of the problems we do in our math talks, warm ups, and examples. These allow every student to be able to take an approach to a problem and reach success. It is helpful because every student can be engaged, and they all get something out of it. The second class concept discussed was using multiple problem solving methods. This is a big basis for the class as a whole, and something we practice pretty much everyday. This is important because not every student will click with every method.

Burdess wants us to understand the important of group work. She stressed that group work can be very beneficial for students in math to bounce ideas and discuss strategy. She said that she found groups of 2-3 students that are not fully the same or fully different works the best. She also talked about moving groups around so students get the full perspective of what they peers do to solve problems. Secondly, we should understand as explained above the importance of multiple methods to solve problems. Lastly, the presenter wants us to make math fun and enjoyable. In the presentation she used a math problem that came from a movie. Using things from life, movies, shows, student interests, etc, in problems is a great way to keep things engaging and fun for students. If students aren't engaged then the problem solving methods they know don't even matter.

Why are low floor high ceiling problems important?
What do you think the benefits of group solving are?

-Max S.

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PD #2: Graham Fletcher: Mathematical Modeling in the Elementary Classroom

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PD #2: Graham Fletcher: Mathematical Modeling in the Elementary Classroom

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Fletcher talked about allowing for guesses, estimation, questions, and wonder, and mentioned the importance of strong mathematical modeling, both of which were important course concepts. He described that it is important for students to figure out what they do and don't know, and really just dissect problems to understand them, and we should not inhibit any curiosity about the context and elements of a problem. He also talked about the importance of in depth mathematical modeling, using different methods of presentation for best understanding, which is one of the main ideas of our course.

Three things he stressed we understand were making sure students understand the full context of problems, letting students be students and kids, and use good modeling practice in our teaching. He said that students often just take numbers out of word problems, and miss the context making it harder to solve so we need to get them to understand the full problem. We need to make sure students understand how the numbers interact and what operations and steps are needed to solve. The other two are explained above.

Why is it important to let students wonder and ponder?
How do we prevent students from just plucking numbers from word problems?

-Max S

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PD Analysis #3: Thomas Moore: Teaching explicitly using manipulatives in Mathematics

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PD Analysis #3: Thomas Moore: Teaching explicitly using manipulatives in Mathematics

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Two things that are parallel to class: The speaker uses an array to demonstrate multiplication, and we have been working on this a lot when talking about decimals. We even just made a video about this for our exam. He also uses a white board to show fractions by dividing a whole up into pieces. We did something similar in class by folding a piece of paper. Lastly, fraction strips were used to demonstrate fractions which was a useful tip we learned in class as well.

Three things math teachers should be doing: We need to attach math skills to a student's knowledge by showing them how to solve problems in many ways. Then, it is more likely to stick with them. By building strong conceptual understandings it is easier for students to move on to more challenging tasks. There are many different manipulatives that teachers can use like blocks, whiteboards, paper, and online tools. If a student does not understand a concept using one tool, we need to explain using another.

Two Questions: What other manipulatives are there to use that we haven't seen yet? Does a hands-on approach work for all elementary math scenarios?

Ellie L

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PD Analysis #2: Michael Minas: The Three Cs of Student Engagement

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PD Analysis #2: Michael Minas: The Three Cs of Student Engagement

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Two things parallel to class: The speaker gives an example of problem solving. In class we have learned many problem-solving strategies like drawing a picture and working backwards. This presentation includes games between students, and we have played collaborative games in class when dealing with certain math concepts as well. Sharing and working with others on problems is much more engaging than working alone in silence.

Three things math teachers should be doing: teachers should be giving students non routine problems that students don’t know how to solve yet. The speaker stresses the importance of “kid-speak” and teachers should take advantage of students teaching other students. One more thing that teachers need to be doing is putting math problems into real life scenarios that link to student, school, world life.

Two Questions: What sorts of problems relate to the lives of students? How do we create an environment where students can collaborate with others but also stay on task?

Ellie L

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3. The speaker touched on using real life word problems to help students understand subtraction, and in class we often talk about using word problems to help students understand fractions, she explained how this can help them visualize the problem better. She also touched on how most kids see subtraction as take away but how that does not help them see a connection to addition and that if we want students to truly understand subtraction there must be a connection to addition. I have seen this in my field experience, the teacher often reiterates that it’s important to see addition in subtraction problems.

4. Three things the presenter hopes that teachers would be more mindful of is: using visuals and models in subtraction problems. Using different subtraction problems such as: add to, take from, put together, take apart, and compare. Also making the connection with addition and subtraction.

5. How do you think you will approach subtraction; will you use any strategies? Do you think it is important to use different strategies in the classroom?

HG

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3. The narrator explains that using models helps immensely with fractions, this especially helps English learners.  We have gone over in class how using models in the class is one of the best ways to help students understand fractions visually. The speaker also touches on how using models and visuals helps with the language gap, students can see what the teacher is explaining without missing out because of language reasons. I have seen in my field experience in an ELL classroom that visuals help a lot when it comes to math, students are able to see the problem and answer using models and it helps them a lot.

4. The presenter hopes that teachers start using models to explain fractions, especially with ELLs, she also hopes that ELL teachers ask students to use their language skills to explain the model they create, and she hopes that teachers use models to show equalities and symbolic representations.

5. How will you explain math when you encounter ELLs in your classroom? Do you think models are the best way to help ELLs understand math why or why not?

HG