Week 1 Reflection Questions

Reflection questions for week one:

What does the term early childhood mathematics mean to you?

I think of early childhood mathematics as the foundation for all math. During early childhood mathematics, children develop their first understandings about numbers, sequences, patterns, shapes, addition, and subtraction. They begin to understand the concepts of adding and subtracting, and should start to become comfortable with simple math. I also think that if a child has positive math experiences in early childhood, he or she will be more open to doing math in the future. I think early childhood mathematics can shape a child's future opinion of math.

What key points did you take from chapter one that inform your understanding of how to teach mathematics for young children?

I took several key points from chapter one that will affect how I will teach mathematics for young children. First, I will take the idea that social interaction and group work can help children develop understanding in math. I would normally think of math as independent work, but after reading the chapter, I can see how discussion and group work would greatly benefit children in learning math. I also like the idea of doing mini-lessons, which the chapter suggests. I think if students engage in mini-lessons over the course of several days, they will develop a greater grasp of a topic and will remember it better than if it is crammed into a single lesson. I also think the point that the chapter makes about focusing on big ideas, rather than small skills, is important. It will be easier to assess a student's understanding of bigger concepts, and will be more important for moving forward that a student understands main ideas.

Challenge 4

Shifts in the students-

Jim has a much better understanding of adding, subtracting, and sequence. Before, he could not count, but now he was able to correctly add 7+6. He also used addition concepts to make more difficult questions easier. He understands that taking away is counting down. He can count down fairly successfully, although a few times he would skip a number.

Lauren already understood the concepts of addition and subtraction, as well as number relationships. This time, she was even quicker in answering the questions. When asked 7+6, she knew the answer was 13, because 7+7 is 14 and 6 is one less than 7. This shows that she understands sequencing, and understands that 7 is one more than 6. She also broke down some of the larger problems into smaller groupings. She understands the concepts of sequences, addition, subtraction.

Elizabeth has also greatly improved in her addition, subtraction, and sequence understanding. She understands that "taking away" is the same as subtraction, or counting down. She understands number relationships, which was demonstrated through the way she solves problems. For example, when solving 6+ _ =15, she knew that 10+6 was 16, and 9 is one less than 10, so 9+6 much be one less than 16, which is 15.

Challenge 3

Initial Thoughts-

Jim did not seem to understand the concepts of addition and subtraction. He was not able to add. One of the two problems he answered correctly was the first one, which asked, "How many do you have if you take away 4 from 6?" He said he "took away 5 and 6," leaving him with four. This shows that he does understand that numbers go in a sequence, and 5 and 6 come after 4. When asked other questions, such as 7+6 and 8+5, Jim guessed random numbers. He was also asked "4-1" and he was correct, saying that "3 comes before 4." Again, this shows that Jim knows the concept of number sequence, but probably only up to about 6 or 7.

Lauren understood the concepts of addition and subtraction. She knew that 7+6=13, by "counting." She next said that 9+6 was 16, and when explaining how she reached that answer, she realized is was actually 15. She understands number sequence, and understands the concept of adding. Lauren could also count backwards, from at least 12 and possibly higher. She understood that subtracting meant taking away, which required counting down.

Elizabeth understands some basic addition, although she had difficulty explaining procedure. For example, she knew that 3+3 was 6, but could not explain it on her own without a prompt. Later, she answers that 4 cows+2 cows is 5 cows, but then changes her answer to 6 when counting out loud. Elizabeth typically tried to answer the questions "in her mind" but when she checked her work using her fingers, she was often able to correct her mistakes. She seemed to understand the concept of addition, but not subtraction. She was not able to answer the subtraction problems correctly. She did not seem to understand that "taking away" was subtracting, which meant counting backwards. She did seem to understand number sequence.

Derek seems to understand the concepts of addition and subtraction. He understands counting sequence, and can count backwards and forwards. However, he said he did not like "high numbers" and probably does not feel comfortable with adding and subtracting past 15. He understood that subtraction meant taking away, and was able to count backwards successfully.

Challenge 2

Challenge 2: How will you get them from where you think they are to where they should be?

There are several instructional activities that I would use to help students move from where they are to where I would like them to be. I would use manipulatives whenever possible so the students can physically see how many of something each different number represents. I could give each student ten flat marbles, and ask them to place two marbles on the right side of their desk. Then I could say, "Add 2 more marbles." Then ask, "How many do you have on the right side now?" I would continue this activity with larger numbers and incorporate subtraction as well. This will be an engaging way for the students to practice simple addition, subtraction, and number relations.

Another activity that I think students would enjoy, which would also help with addition and subtraction, would be having them come up with about five to ten addition and subtraction problems on their own, using numbers 1-20, which they will trade with a classmate. Then, after they trade and complete the problems, they will trade back and check their classmates work. This will allow them to be interactive.

Other activities might include incorporating everyday objects into addition and subtraction. Using numbers from student's personal lives, such as how many siblings they have, and letting them compare will make them more interested than if they were just working with numbers without any personal significance.

As time progresses, I will observe how students understanding of numbers changes. I can do this by using the same activities but making them more challenging.

Challenge 1

Challenge 1: What do you think first grade students can do related to numbers, number relationships, and addition and subtraction with sums less than 20 coming into 1st Grade?

I think students coming into first grade should be able to count to twenty and should be able to understand that 2 is more than 1, 3 is more than 2, etc. They should be able to put cards with a different number of objects in order, meaning if they were given three cards, the first with one picture of a bear, the second with two pictures of bears, and the third with three, they should be able to determine which one has the most bears and which one has the least. They should be able to tell how many more bears are on the card with three than on the card with two by doing simple subtraction.

Students coming into first grade should understand addition in the way that if you ask them how many pets they have if they have one cat and one dog, they should be able to say "two." They should be able to do the same with subtraction. They should also be able to recognize what the numbers one through twenty represent and what they look like, and understand that the symbols represent a number.