Writing 5: Peach Plains

• 12/3 Peach Plains Experience

As future teachers, any time in a classroom is considered valuable. Getting experience in a variety of environments, with an array of students gives insight, and provides inspiration for activities and teaching practices. Peach Plains in particular has a very interesting environment. It seems to have a rather open concept in the classroom, with motion permitting furniture. This has proven to be beneficial for students to move naturally and not feel so confined, and it surprises me that more classrooms do not follow this model. I work in a public school system for a before and after school program, and things (from the outside) seem rather traditional. Therefore, the time spent at Peach Plains Elementary School is definitely worthwhile.

Just from mere observation, the Peach Plains classroom has interesting factors that make it a comfortable learning environment. Aside from the fascinating physical structure of the classroom, the way the teacher runs her classroom is extremely innovative and incorporates individual thinking. If one hears that students have a journal for language arts, you would not think twice. However, they had math journals, where they could record their mathematical questions, findings, and scratch-work. I had never been introduced to this, and they seemed to find it very helpful. It was held to the same standard as a writing journal and it is something I plan to carry into my future classroom.

There were many valuable aspects to the Peach Plains experience, but my favorite piece of math/teaching of math was they way students were taught how to multiply double digit numbers if they were stuck. The numbers were broken down into four chambers, and then multiplied based on their columns. Then, once all of the answers were found, they were added, and you got the correct final answer (example below showing it better than I can explain it). This was helpful for two students in my group, who struggled doing the problem without breaking it down. This stressed and exemplified my understanding that children are all different. Yes, there is no particular "math gene" and everyone is capable of doing math, but everyone learns at different paces and in their own way. I could relate to this because math was not my strong suit, and this would have been helpful for me as a child. I highly recommend this method and plan to use it if I get the chance.

The NCTM’s Effective Mathematics Teaching Practice that I am focusing on is: "Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments."
One of the most important things that I have come to understand in this entire class is that mathematics is a struggling subject, in the sense that we do not discuss answers or methods. It is perceived that there is one way to do problems, and there is no gray area between right and wrong. I did not feel that this was the case for the fourth grade classroom we were in. The posed question was simply, "How many skittles are in the jar?" Then, we allowed time for students to decide their own approach to the problem. After this, the students were allowed compare and contrast their ideas and deem which was most effective. This promoted healthy communication and reasoning skills. It also showed how differently and similarly children think. My group all had the same method: take the number of skittles in an individual package and multiply it by an estimated amount of packages total. Other groups however, decided that it was best just to guess the amount, and others looked at how full one package made the bottom of the jar, and then estimated from there. All methods are useful with such an open-ended question.

Overall, going to Peach Plains is always a pleasure and this experience was no exception. It further proved how valuable mathematical conversation is, especially with the creative minds of young students.

Writing #4: Family Math Nights

FAMILY MATH NIGHT

Madison Stieber

Meghan Milarch 

Food Bingo!

Materials:

• Flashcards with drawn pictures of food 
• Flashcards with attributes to food that we read off 
• Different colored chips for each player (red and yellow, given by professor)
• Poster 

Procedure:

• Pass out materials 

• 16 flashcards with pictures of food
• Different colors of chips  

• Explain game 

• We arrange the cards like a 4x4 bingo board.
• We will let the players pick their favorite food or least favorite food for their “free space”.
• We describe the attributes of a food, and they place a chip on the card they think best fits the description.
• There are no right or wrong answers!
• They need to get four in a row (diagonal, horizontal, or vertical) to win.
• Although there are no right or wrong answers, we are allowed to ask them why they chose the food that they did and defend it. If they cannot think of a reason aside from getting a bingo, we will give them the opportunity to pick a different food.

16 Foods

• Cake 
• Pizza 
• Apples 
• Grapes
• Carrots 
• Broccoli
• Chicken
• Turkey
• Pickles
• Milk
• Cheese
• Bread
• Eggs
• Butter
• Cookies
• Tomato 

• We feel that this is an interesting and fun activity because it allows kids to be strategic and pick what answer to which question will allow them to get a bingo.
• They use math through mentally categorizing the food to fit our description.

Stories

#1: This took place on the first Family Math Night. This stood out to me in particular because when making the game, we chose rather basic attributes that we thought could apply to anyone. However, this instance showed me the importance of cultural differences.

A family of four came up to us wanting to play the game: a mom, a dad, and two brothers. The parents spoke Spanish to the children, and the kids spoke English to us. More than once, an attribute did not apply to the children, so we had to make one up or choose a new one. In particular, one of our attributes were, "What is something you would put on a hamburger?" We expected them to lay a chip on cheese, tomato, pickle, etc. Without question, the oldest boy placed his chip on eggs. When I asked him to defend it, he said it is what he gets from McDonald's. I glanced at his mom, and she said, "He means an egg mcmuffin." While I found it funny, it showed me how children make connections and in this case, associate American foods to what they have ate, even if they have not ate the thing itself. Obviously, we let him keep the answer because we really appreciated him making that connection and it was very clever.

#2: This is not necessarily a specific story, but more of a general observation. The first location was fun with the kids, but it was as if they were just going through the motions. All of the games were in one big room, staring at them right as they walked in, and I could understand if it was a little overwhelming. The second time, kids were very engaged. There was a nice flow of people with how this was set up and actual mathematical conversation and debating took place. Children thought of ways attributes could apply to food that I had not thought of. For example, a child was asked to put their chip on something you use for baking. She was looking for a bingo and put a chip on a tomato. I asked her what she meant by it, and she said, "You put tomatoes on pizza, and then you bake pizza. BINGO!" There were multiple cases of this, and the younger children were very proud of themselves when they got a bingo. Students also did not act as if their parents forced them to come; they genuinely seemed to want to play the games.

Conclusion

Fun: I thought the game was fun for the majority of kids. Younger kids enjoyed it and often did it once by themselves, and played again against an opponent. Older students enjoyed the sense of competition, whether they played with another student or one of us. I do think that this would be best for a younger classroom though, because a few older students I feel were not mathematically stimulated. They had fun, but the math was too simple for them to appreciate it.

Mathematical Thinking: I saw mathematical thinking when students were multitasking. To be specific, they were strategic as to how to get four in a row, while also trying to fit the attribute. I was surprised by how many students did not try to stretch the attribute just to win, but rather gave a solid defense to their answers. Some answers we had not even thought of ahead of time. I was also surprised as to how many students forgot that the goal was to get a bingo; some enjoyed just discussing their answers.

Takeaway: This entire experience was fun because we got to not only work with kids, but get an idea as to what they enjoy. From this, I can say that students do not always shy away from challenges and they appreciate competition. Our game was not originally a competition and it would have been very boring without it. In addition, I would include more of a variety of cultural food, so no one would feel left out and we could maybe extend students knowledge. Finally, if I were to use this for older grades, I would incorporate more cards. What I do love about this game, is that it is adaptable to many other subjects, such as our original plan to have equations on cards. 

Overall, this was a great experience with many takeaways that I can apply to my future classroom!

Blog 3

Being able to go to the elementary school was a great experience! Any opportunity to work with students is extremely valuable. I feel that the lesson was well thought out and organized on paper, but many questions came up as we went. For example, some groups cut out two feet to measure, while others used one. While that is not major, there was still a level of uncertainty. It all worked out in the end. 

I saw a lot of mathematical thinking among the students. A question I asked frequently was when their foot did not land perfectly, whether they thought it was a half or quarter. Some suggested something without a prompt, while others rounded up or down to an exact foot. When I asked them to be more specific, they were able to determine a quarter or half. I also saw them struggle with converting feet to inches, including not knowing that a ruler equaled one foot (12 inches). To my delight, once they were reminded what a foot equaled, it was like a light turned on and they remembered. In addition, I asked them where the half inch hash on the ruler was, and from there, they could determine the quarter inch hash. All in all, they needed guidance, but were by no means completely lost.   

There are a couple things I would have done differently. To start, I would have rather had them walk heal-to-toe to measure certain things. While this could make finding perimeter difficult, I like the idea of keeping them moving and doing just the lengths of certain things. This could also move things along quicker so we could spend more time analyzing they data. Besides that, I wished we could have been outside, but no one can control the weather. Overall, I believe it was a great success and I give major credit to the people that took charge in the classroom, and also those who found other things to measure since it was raining outside. 

Growing up, I do not distinctly remember doing anything fun in math. It was rather boring and I think that stretches to now, because I do not enjoy math. What this has showed me, is that the experience is almost as important as the content. What I need to do next, is to consider ways to make math more interactive and memorable. They can have positive thoughts on their math experiences, and the content itself will be remembered better.

I am grateful to work with students at any point, and the staff was very friendly. These students were smart and had many good ideas. As I said before, they were no where near lost in the material, rather they just needed guidance. In conclusion, my largest takeaway is that when I have my classroom, I will strive to make a more enjoyable and interactive math environment. 

Writing 2

To begin, I had started using Venn diagrams at a young age. The purpose of them was rather clear to me, and I actually used it as a studying technique in elementary school. However, I lost touch with them throughout high school, and this class was the first time I had used them again. As I thought I understood their purpose, I interpreted it wrong my first time making my own. I thought the middle was an in-between level between the right and left circle, when in reality, it is a section designated for something that has the traits of both the left and the right circle.

My initial intention with writing this blog was to find a lesson plan using a Venn diagram, and describe its significance. Research led me to the link at the very bottom, where it reiterated what a Venn diagram was and its purpose. However, the example it used sparked an idea: I put too much time into my attribute cards for them to just sit in my binder. I used my cards for "On-Off the Bus," but now I realized I could use them to make my own Venn diagram and understand what I did wrong the first time. I decided to make my own diagram with Apple phone cords to show what I originally did wrong, and what it is supposed to be.

The picture above will not upload clearer, but this is the incorrect example. On the left there are mammals (giraffe, gorilla, kangaroo, dolphin), the middle are birds (toucan, ostrich, flamingo, parrot) and the right are reptiles (snake, lizard, crocodile, iguana). While these are organized in the correct categories, they defeat the purpose of a Venn diagram and the middle circle does not have shared similarities.

This is organized correctly and it reinforced to me the purpose of a Venn diagram. The left has mammals (giraffe, kangaroo, gorilla), the right has aquatic animals (shark, fish, seahorse), and the middle has sea mammals (dolphin, walrus, killer whale). The middle shares a characteristic with the left, which is having lungs, and it shares a characteristic with the right, which is that they live in the water.

Math is broadly defined as a subject in which we recognize patterns and categorize things. This could serve as a great activity for elementary math. Allowing students to make their own attribute cards would let them use their creativity, while using the Venn diagram can help them study and categorize. While it was used for science in this example, math was involved because there is an even number in each circle to categorize and place the cards in the correct place. Overall, the Venn diagram is a useful tool stemming from math, that can reach into other subject areas.

https://www.brighthubeducation.com/lesson-plans-grades-3-5/43208-lesson-on-using-venn-diagrams-for-math/

#1: First Impressions

Introduction:

I am very surprised as to what activities constitute as math. I thought this class was going to be about simple equations and the basics of math, specifically regarding numbers. As we do more activities, such as pentomino activities, creating patters, etc., I see how much goes into teaching lower level learning, but how strongly it applies to more difficult learning. It's teaching the importance of logical thinking. So many of these activities are great for the classroom.

https://www.pre-kpages.com/pattern-block-mats-for-preschool/
The link above is a lesson plan that I thoroughly enjoyed and it uses patterned blocks. It introduces problem solving skills to young children and is an activity young learners would find fun. Specifically, it says:

"Consistent use of pattern blocks in the early childhood classroom can help develop these important math skills:

• Recognize and describe two-dimensional shapes

• Comparison

• Visual Discrimination

• Recognize and describe three-dimensional shapes

• Angles"

These are all vital skills, and the activity does not require a crazy amount of materials.

Mathematical Autobiography:

I remember preschool-1st grade math was heavily based on finding patterns. I feel my teachers did a great job explaining how they can be found everywhere. I do not remember specifics, but I remember finding them at home on dishtowels. However, jumping to middle/high school, my teachers taught for a test score and not mastery. I was not strong in algebra or geometry, and my teachers looked for a passing grade. Material wasn't revisited if we got it wrong. In particular, over 50% of my geometry class did not understand proofs, and the teacher said, "These are not important, they won't be on your SAT." Then, we got one on our test for that chapter. I was pleasantly surprised at how much my freshman year Algebra 110 professor (college freshman) helped me and truly wanted me to understand what I was doing. It was totally backwards for me.  I feel I would have been less lost when I first came into college if my teachers in high school cared more about individuals, as well as the majority. I understand that it is impossible to accommodate to every single need though. There needed to be a balance.