Reflection Questions: Week One

What does the term early childhood mathematics mean to you?

The term early childhood mathematics refers to the basic mathematical skills and fundamentals that should be introduced and understood during the early years of a child's life. They are the building blocks for a child's understanding of mathematics. Early childhood mathematics introduce both skills and concepts that will later be used when a child begins to learn higher levels of mathematics.



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

A key point that stood out to me stressed the importance of not teaching students by telling, but implied that we must help them construct their own ideas using the ideas that they already own. However, it is important to understand that the manner in which you conduct your class plays a crucial role in what your students learn and how well the information they learn is understood. It is important that the teacher understands that the factors that influence learning are influenced by the teacher and will impact what and how well students learn the content being taught.

I also found that by having the children within the classroom engage in interactive classroom activities will provide the students with opportunities to learn from each other. It will also provide the students with "an enviornment to share ideas and results, compare and evaluate strategies, challenge results, determine the validity of answers, and negotiate ideas on which all can agree."

As a teacher, it is important that I understand the use of manipulatives and their role in either helping or failing to help students construct ideas. The use of tools is good when used correctly and appropriately. It is important that I provide students with the necessary tools, models, and materials to learn mathematics effectively but a key point mentioned within the chapter stressed the importance of knowing how to use such tools correctly. The chapter mentioned the importance of the teacher introducing the models appropriately and "perhaps conducting a simple activity that illustrates this use".

From the reading of chapter one, I also found that it is important for the teacher to understand the value of teaching with problems and the effectiveness of problem solving. Problem-based teaching seems to be an approach that can be quite confusing or difficult yet highly rewarding for the students and teacher. I also found that there is a 3-Part fomat for problem-based lessons that can be followed.

A helpful point made when discussing how to deal with a class that doesn't understand the content being taught was to "not give into the temptation to show them but rather regroup and offer students a simpler related problem that will help them prepare for a more difficult one." It stated that the teacher should first find out what ideas the student of group has and try and provide hints on ideas that you hear are being considered within the group of students.

Challenge 4

The children seemed to possess higher level thinking during the second set of interviews. The children overall seemed more capable of counting in their head or understanding the concept behind addition and subtraction. They were able to use information that they already understood or had previously learned and used it in their thinking when solving the addition or subtraction problem presented. For example, Lauren understood that 7+6=13 because she already knew that 7+7=14 and knew that if it were 7+6 then it should equal up less than 14 so she thought it should be 13.

The children also appeared to understand what they were being asked and were more open to answering the questions. During the first set of interviews, the children seemed more confused when asked particular questions and would simply answer that they didn't know or wouldn't have a good explanation behind their reasoning. Even if a child didn't know the answer to a question asked, the child would at least think about the question being asked and try and figure out the answer rather than give up like they seemed more likely to do in the first set of interviews.

Challenge 3

I think it is important to understand that each child doesn't learn things the same way or at the same rate. It is important to provide those who learn best visually with a visual activities so that they can understand the concept of addition and subtraction better. It is important to understand how each child does learn material so that I could provide the child with an activity that would accomodate for his/her needs. From the videos, I had the opportunity to see that some children within the class performed subtraction by counting backwards while others just guessed or based their answer on a "pattern" that they had previously seen. If this were my classroom of students, I would seperate each child into a group of students that seemed to perform addition or subtraction using the same method. I would also find lesson ideas and activities that incorporated all methods of perfoming addition and subtraction so students could understand that there is more than one way to figure out the answer. I believe it is important to address each child's needs and by having a child exposed to different learning styles or options, the child is more likely to catch on and figure out the style that works best for them.

If I were a teacher of this class, I would build on the concept of what it means to subtract from a higher number or simiply add to it. I would explain the idea of combining numbers and how to distinguish between when it is necessary to count forwards or backwards. I would incorporate the use of a visual but also have the child practice solving simple math problems using their fingers or by counting in their head without having to use their fingers. I would provide the child with mulitple options and slowly take them away until they have reached the point where they do not need a visual aid to help them solve the problem.

Challenge 2

It is important to provide students with an array of activities that allow the child to become actively engaged in learning. Providing students with the use of pattern blocks, counting bears, and hands-on activities will allow the students to get engaged with the activity. It will give them the opportunity to practice basic counting, adding/subtracting numbers, grouping and will help them build on what they already understand so that they can begin to recognize more complex shapes, patterns, addition/subtraction problems and will also have the opportunity to understand how basic shapes can be used to make other shapes. It is important to incorporate group and student led instructions so that the students can work cooperatively with others to build on information they already know. It is important for students to work together so that they can begin to think critically and have the opportunity to build on what other students may know. It is also important to integrate math into other subjects and provide students with fun learning games that catch their attention.

Challenge 1

Coming into first grade, students are capable of doing basic addition and subraction skills. They have the ability to add and subtract single digit numbers and understand the concept of "taking away". They have the ability to understand and develop basic patterns using numbers, colors, and shapes. They understand and have the ability to perform basic number counting; counting up to 20. Also, they can recognize basic shapes. They understand the concept of "multiples" and how to group items by number.