Reflection Questions Week One

1. What does the term "early childhood mathematics" mean to you?
I believe that early childhood mathematics is the most important mathematics that children have. It sets the foundation for all of their math knowledge for their academic future. This is the time that students learn the most and that their brains are the most absorbent. Setting the foundation for math includes teaching the students their numbers, what each number represents, and how to add and subtract their numbers.

2. What key points did you take from chapter one that inform your understanding of how to teach mathematics for young children?
-p. 4- Three Factors that Influence Learning
-student reflective learning
- social interaction with other students in the classroom
-use of models or tools for learning.
I like this because it teaches me what factors are important to implement in my students learning every day.
-p.7-9- These few pages talk about Models, and how important they are in teaching math. All students need to see things visually and be able to manipulate objects and models help accomplish this task.
-p.14-19 describe problem based approaches to teaching. Each of these pages discuss a different part of the problem solving approach. Before, During, and After. These pages are very important to teach me HOW to approach problems with the children, and what steps to take before assigning the problem, as well as after.
-p.20-21-I loved how these pages answered frequently asked questions. It was helpful to know how to assess different strategies and types of responses I'll get from the students.

Challenge 4

Jim- Post teaching, Jim was able to group numbers, could count forwards and backwards, and also had his doubles facts (ex. 7+7=14) memorized. Jim has learned a lot this year. He is more proficient in all of his skills.

Lauren-Lauren has also learned a lot in first grade. She knows all her doubles facts by memory, and is also able to realize that because the answer is less, then one of the numbers in the problems must be less. ex. If 7+7=14 then 7+6=13. She does understand all of her processes, but she still isn't able to explain the process in words.

Elizabeth-Elizabeth is also familiar with her doubles facts. However, she doesn't process problems in her head-she still needs to count on her fingers. She does understand the process and is able to explain her reasoning.

Challenge 3

Jim- Jim tried to strategize during his testing, but ended up guessing several times. He was throwing out random numbers and not really thinking about how his answer would make sense. However, he did know at one point in the video that "3 comes before 4". As Jim's teacher, I would focus heavily on the concept of a number. I would not only re-evaluate his knowledge of what number comes in what order, but I'd also evaluate his knowledge of conservation. I would stress that he knew that the number 3 represented three (1.2.3) cookies, or three stuffed animals. After this, I would be sure that he understands what the concept of addition and subtracting is. That he knows when he sees the problem 3 + 1 that you are adding one more cookie to the 1.2.3 cookies you already have.

Lauren-Lauren recognizes patterns that she's learned before. She isn't really sure how to explain the patterns, but it's clear that she has previous knowledge of them. She also proved that she knows how to count forward and backwards. If I were Lauren's teacher, I would work really hard with reinforcing her counting skills and then show her how that relates to addition and subtraction.

Elizabeth-Elizabeth can solve most of the problems, but she can't explain how she solved them. She is able to count forwards and understands that 6 is after 7 to solve a problem. She was often confused at whether she was supposed to be adding or subtracting. As Elizabeth's teacher, I would be sure to create some sort of illustration that helps her to visualize the meaning of "subtraction" and "addition" whenever she sees the signs or hears the words "plus", "minus", "add", and "take away".

Derek-Derek is able to count forwards and backwards. As he solves problems we see that he is using his fingers as manipulatives and relies on them in order to count. He proves to be better with addition than subtraction. For Derek, I would provide him other sorts of manipulatives rather than his fingers so that he can learn to count objects and be knowledgeable about conservation. I would also reinforce addition and subtraction with smaller numbers before challenging him with harder larger number problems.

Challenge 2

I would use playing cards, blocks, pick up sticks, and flashcards initially. Playing cards are good for number identification-they can see what the number is as well as count the number of each sign (heart, club, spade, diamond) on each card. You can play games such as, Go Fish, War, and Memory all with playing cards, and as the children become more advanced with their number memorization and concepts, you can even let them add or subtract the two numbers on the cards. With blocks, students can use them as their adding or subtracting manipulatives-they can match each number of blocks to it's corresponding written number. With Pick-Up-Sticks, children can take turns playing the actual game, and then count the individual colors of sticks they won, and then add or subtract them with their opponent. Flashcards are always good, just to keep the children on their toes with number identification, adding, and subtracting and keep it at a steady pace. These are always good for downtime with the children.

Challenge 1

When First Grade students first enter the classroom, I think that they are able to identify their numbers 1-20 and recognize which numbers are more or less. They should also be able to put numbers in sequence.
I think that in first grade they will be learning to add and subtract, as well as count higher. By the end of first grade, a good goal would be to have the children able to add one digit numbers with a sum up to 20.