Week 1, Chapter 1

1. When I think of early childhood math, I don't think so much about learning skills as I do about recognizing patterns and learning how to think logically. Especially in the younger grades, I think children should focus on learning their shapes, making patterns with colors, learning how the shapes fit together, and learning how to solve problems on their own. Problem solving is the basis to all math.

2. One major point this chapter made is that children learn through reflective thinking, social interactions, and hands-on learning. They need time to work together and learn from each other, but also to think quietly to understand what they have learned and make sense of it. It is important to establish an open, trusting classroom so that children feel comfortable making mistakes and sharing their ideas with me and the other children.

Chapter 1 also suggests helpful ways to teach by solving problems, but before even beginning, the problem must "begin where the students are" in both life experience and skills attained so that the problematic portion is the math, not the question.

Not only that, but you have to prepare the children for problem-solving. Before problem-solving, the teacher must establish expectations and explain the problem thoroughly. During the problem-solving, the teacher should never show a student how to solve a problem, only provide hints or "pieces" of the solution and talk the student through the solving process with encouragement. Praise can be negative feedback for the ones not receiving it, so use it cautiously. Instead of one-on-one time, perhaps engage the students in a full class discussion so they can agree on the solution together and not rely on the teacher.

Letting students explain things to each other allows for a more open and positive experience because teachers words are often taken concretely; when talking to other students, they can question and disagree without feeling disrespectful or "wrong."

Assessments such as rubrics and interviews are useful in mathematics. Rubrics are a good way to grade assignments based on understanding and accomplishment; i.e. how much of this project was completed, and how much was completed correctly? Diagnostic interviews are one-on-one discussions to gauge a child's thinking process about a subject.