Reflection Day 22 (Math Methods Day 4)
Reflection on book (Early Childhood Mathematics)
--- Data Analysis (Graphing and Probability) ---
“Toddlers recognize differences between things…They observe, compare, and categorize things that go together from things that don’t fit the category” (p. 128).
“Children organize the data into simple bar graphs and discuss what they found” (0. 128).
Daily Graphing Activities
“The NCTM Standards present the topic of graphing: a graph presents numerical information visually” (p. 128).
The Challenge in Reading Graphs
“Graphs are a widely used means of presenting information” (p. 130).
“Early graphing experiences rely on simple displays where comparing and counting help children succeed” (p. 131).
- Reading a graph uses two questions: 1) comparing questions and 2) counting questions
Early Experiences with Graphing
“Very young children (3- to 5-year-olds) spend time comparing, sorting, and classifying everyday object” (p. 131).
Scoop and graph Objects
The teacher prepares a re-usable mat of columns and cells. Children work individually or in team and “scoop” a small number of coins. The coins are sorted and arranged on the mat.
Picture Graph
“A picture graph is a transition from the real object graph to the symbolic graph. Pictures are cut and assembled into a graph”
Bar Graphs and Circle Graphs
In the bar graphs, teachers make the transition from real objects to pictures and then to symbols.
*Like Montessori’s beans
In circle graphs, it challenges students to think in 360* --- telling time, measuring the circumference.
Line Graphs
“Children need many experiences with mapping and following routine before they grasp the meaning of line graph” --- ex) class attendance by month
*Like Montessori’s pre number activities. ex) sorting, shapes
--- Assessment ---
“In 2003, the NCTM issued a position statement that warned that a student’s career or advancement, or an entire school’s existence, should not be based on a single test” (p. 32).
*Don’t ‘teach to the test’ – use formative assessments like 3 period lesson
“Speed has very little to do with mathematical ability. Speed emphasizes powerful memory over understanding the concept, and is not how mathematics work” (p. 33).
Assessment and Evaluation (p. 35)
- How is the student learning?
- How is the class learning?
- How does the teacher write a progress repeat for child?
- How is the store progressing?
Assessment Strategies (p. 36-37)
- Observation
- Interview
- Performance tasks
- Student writing
- Portfolio
“A beginning teacher needs to keep and preview portfolios before it is possible to compare samples and get ideas for grading” (p. 47).
“Over time, certain patterns will emerge that set criteria for excellence” (p. 47).
*both quote stress importance of creating mathematics portfolios for each child.
IEP ---> for children who are more challenged:
- give additional time
- shorter assignments
- get the child’s attention
- have patience
- Avoid timed tasks as a measure of proficiency
- Speak clearly and slowly
Reflection on book (Early Childhood Mathematics)
--- Data Analysis (Graphing and Probability) ---
“Toddlers recognize differences between things…They observe, compare, and categorize things that go together from things that don’t fit the category” (p. 128).
“Children organize the data into simple bar graphs and discuss what they found” (0. 128).
Daily Graphing Activities
“The NCTM Standards present the topic of graphing: a graph presents numerical information visually” (p. 128).
The Challenge in Reading Graphs
“Graphs are a widely used means of presenting information” (p. 130).
“Early graphing experiences rely on simple displays where comparing and counting help children succeed” (p. 131).
- Reading a graph uses two questions: 1) comparing questions and 2) counting questions
Early Experiences with Graphing
“Very young children (3- to 5-year-olds) spend time comparing, sorting, and classifying everyday object” (p. 131).
Scoop and graph Objects
The teacher prepares a re-usable mat of columns and cells. Children work individually or in team and “scoop” a small number of coins. The coins are sorted and arranged on the mat.
Picture Graph
“A picture graph is a transition from the real object graph to the symbolic graph. Pictures are cut and assembled into a graph”
Bar Graphs and Circle Graphs
In the bar graphs, teachers make the transition from real objects to pictures and then to symbols.
*Like Montessori’s beans
In circle graphs, it challenges students to think in 360* --- telling time, measuring the circumference.
Line Graphs
“Children need many experiences with mapping and following routine before they grasp the meaning of line graph” --- ex) class attendance by month
*Like Montessori’s pre number activities. ex) sorting, shapes
--- Assessment ---
“In 2003, the NCTM issued a position statement that warned that a student’s career or advancement, or an entire school’s existence, should not be based on a single test” (p. 32).
*Don’t ‘teach to the test’ – use formative assessments like 3 period lesson
“Speed has very little to do with mathematical ability. Speed emphasizes powerful memory over understanding the concept, and is not how mathematics work” (p. 33).
Assessment and Evaluation (p. 35)
- How is the student learning?
- How is the class learning?
- How does the teacher write a progress repeat for child?
- How is the store progressing?
Assessment Strategies (p. 36-37)
- Observation
- Interview
- Performance tasks
- Student writing
- Portfolio
“A beginning teacher needs to keep and preview portfolios before it is possible to compare samples and get ideas for grading” (p. 47).
“Over time, certain patterns will emerge that set criteria for excellence” (p. 47).
*both quote stress importance of creating mathematics portfolios for each child.
IEP ---> for children who are more challenged:
- give additional time
- shorter assignments
- get the child’s attention
- have patience
- Avoid timed tasks as a measure of proficiency
- Speak clearly and slowly