Reflection Day 19 (Math Methods Day 1)
Reflection on books
--- Foundations, Principles, and Standards ---
English language learners (ELL)
- Need help with math terminology.
- “Speaking clearly and at a reasonable pace helps students comprehend the language” (p. 2).
- Use “Think-Pair-Shares”
Gifted Children (p. 3)
- Set up with a mentor
- Take higher level math
Learning Disabilities (p. 4)
- Repeat directions, make sure they understand
- Help with reading, or give them a partner
- Make classroom calm and simple – not overstimulating
Piaget, Vygotsky, Bruner, and Dienes
“Their ideas form the basis for constructivism, a theory that views the child as creating knowledge by acting on experience gained from the world and then finding meaning in it” (p. 10).
Piaget: focus on the child’s thinking and the process, not just the answer.
Vygotsky: natural and cultural development through human and environmental interaction
- Zone of proximal development; tasks child cannot yet do without help
- Scaffolding; support and guidance
--- Planning for Success ---
“There are three key ingredients to a successful beginning: a well-prepared environment, a developmentally appropriate math curriculum, and you” (p. 15). *the role of the teacher
Free choice must be reinstated for a short time so that learning can proceed (p. 17). *Montessori philosophy
Teachers need to be flexible “student may also want to work together to solve a problem”(p.19). some students work better in groups, others on their own.
“As you refine your skills and learn from the children, the necessary keys to success will unfold. The process is never ending, but the journey is worth taking” (p. 29).
--- The Language of Math (Communication and Representation) ---
“The challenge to the teacher is to take the powerful tools of the language of math and guide the child to a deeper understanding based on what is already known…we will explore a different math strand and discuss how you can achieve the delicate balance between guiding learning without overwhelming the child, or subjecting the child to meaningless drill” (p. 66).
*Developing preschool math language;
1) using song and verse
2) through children’s literature
--- Early Math Concepts (Matching, Classification, Comparing, and Ordering or Seriation) ---
“According to Piaget, physical knowledge about color, size, shape, and texture can be used to construct logico-mathematical knowledge” (p. 72).
Matching
“Matching is the concept of one-to-one correspondence” (p. 72).
“Children as young as 2 grasp the intuitive notion of things being added or taken away” (p. 73).
Four dimensions the teacher considers; 1) are the item identical or different? 2) are there many items to match or just a few? 3) is there the same number in each set? and 4) are the sets “joined or not joined”? (p. 73)
“Every routines provide many opportunities for matching… By the age of 4, most children are able to match objects” (p. 76).
With concrete objects it’s helpful to line thing up in horizontal rows to show the problem clearly.
Performance assessment can be done in
- Identical sets
- Equivalent sets
- Classification (sameness)
- Comparing (difference)
*note to self: when children are asked to create sets they usually sort objects first by color.
Reflection on books
--- Foundations, Principles, and Standards ---
English language learners (ELL)
- Need help with math terminology.
- “Speaking clearly and at a reasonable pace helps students comprehend the language” (p. 2).
- Use “Think-Pair-Shares”
Gifted Children (p. 3)
- Set up with a mentor
- Take higher level math
Learning Disabilities (p. 4)
- Repeat directions, make sure they understand
- Help with reading, or give them a partner
- Make classroom calm and simple – not overstimulating
Piaget, Vygotsky, Bruner, and Dienes
“Their ideas form the basis for constructivism, a theory that views the child as creating knowledge by acting on experience gained from the world and then finding meaning in it” (p. 10).
Piaget: focus on the child’s thinking and the process, not just the answer.
Vygotsky: natural and cultural development through human and environmental interaction
- Zone of proximal development; tasks child cannot yet do without help
- Scaffolding; support and guidance
--- Planning for Success ---
“There are three key ingredients to a successful beginning: a well-prepared environment, a developmentally appropriate math curriculum, and you” (p. 15). *the role of the teacher
Free choice must be reinstated for a short time so that learning can proceed (p. 17). *Montessori philosophy
Teachers need to be flexible “student may also want to work together to solve a problem”(p.19). some students work better in groups, others on their own.
“As you refine your skills and learn from the children, the necessary keys to success will unfold. The process is never ending, but the journey is worth taking” (p. 29).
--- The Language of Math (Communication and Representation) ---
“The challenge to the teacher is to take the powerful tools of the language of math and guide the child to a deeper understanding based on what is already known…we will explore a different math strand and discuss how you can achieve the delicate balance between guiding learning without overwhelming the child, or subjecting the child to meaningless drill” (p. 66).
*Developing preschool math language;
1) using song and verse
2) through children’s literature
--- Early Math Concepts (Matching, Classification, Comparing, and Ordering or Seriation) ---
“According to Piaget, physical knowledge about color, size, shape, and texture can be used to construct logico-mathematical knowledge” (p. 72).
Matching
“Matching is the concept of one-to-one correspondence” (p. 72).
“Children as young as 2 grasp the intuitive notion of things being added or taken away” (p. 73).
Four dimensions the teacher considers; 1) are the item identical or different? 2) are there many items to match or just a few? 3) is there the same number in each set? and 4) are the sets “joined or not joined”? (p. 73)
“Every routines provide many opportunities for matching… By the age of 4, most children are able to match objects” (p. 76).
With concrete objects it’s helpful to line thing up in horizontal rows to show the problem clearly.
Performance assessment can be done in
- Identical sets
- Equivalent sets
- Classification (sameness)
- Comparing (difference)
*note to self: when children are asked to create sets they usually sort objects first by color.