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Math 204: Exam Review 1

General Pedagogy

Question: Name and describe the six principles.
Answer: 1. Equity/Equality: high expectations and strong support for all
2. Curriculum: Must be cohesive and continuous, builds over time, vertical and horizontal
3. Teaching: teacher must have strong understanding, process vs. product
4. Learning: all students learn at different paces; understanding is essential
5. Assessment: ongoing assessment; design with the end in mind
6. technology: when and how often to use it; calculators


Question: Name and describe the six content principles.
Answer: 1. Numbers and Operations: Pre-number concepts, adding, subtracting, multiplying, dividing of whole numbers, fractions and decimals
2. Algebra: Algebraic thinking
3. geometry: Geometric thinking
4. Measurement: most ignore, must incorporate throughout
5. Data Analysis and Probablility


Question: Name and describe the process standards.
Answer: 1. Problem-Solving: Use what students know and build and apply to new knowledge
2. Reasoning and Proof: Use and develop reasoning skills, teacher must model thinking
3. Communication: Can student explain their thinking to others?
4. Connections: connecting topic to others in math and other subjects
5. Representations: Using manipulatives


Question: What is the definition of math?
Answer: Science of pattern and order
- Process of figuring things out


Question: What are the implications for teaching?
Answer: -Build new knowledge from prior knowledge 
-Build Opportunities for reflective thought
-Provide Opportunities to talk about math
-Treat errors as opportunities to learn
- Use multiple approaches
- Scaffold new content
- Honor Diversity


Vocabulary

Question: What is rote?
Answer: Children can count but have no idea of what each number means. 

Question: One- to One correspondance
Answer: Ability to count one number for each item or movement

Question: Subitizing
Answer: ability to look at an amount and just know how many it is

Question: What is Cardinality?
Answer: Knowing that the last number you count is the total of what you counted; understanding that numbers are embedded within

Question: What is the difference between relational and linear (instrumental) understanding?
Answer: Relational: Have multiple concepts inter joined to create depth of conceptual understanding

Linear: one or two networks


Piaget and Vygotsky

Question: What were Piaget's main ideas?
Answer: -Cognitive Development: children need to have time to reach certain stages of development in order to be able to master certain milestones
-Assimilation: characteristics that a person attributes to a particular object
- Accommodation: changes in the characteristics that a person makes to create a new schema
- Schema
- Reflective thought


Question: What were Vygotsky's main ideas?
Answer: - Social Development Theory: stresses role of social interactions in the development of cognition
-Zone of Proximal Development
-places more emphasis on culture sharing
- social factors contribute to cognitive development
-cooperative learning


Question: Name and describe Piaget's stages of development
Answer: 1. Sensory- Motor (birth- 2 years): recognizes self as agent of actino and begins to act intentionally
2. Pre- Operational (2-7 years): Learns to use language and to represent objects by images and words; thinking is still egocentric; classifies an object by a single feature
3. Concrete Operational (7-11 years): can think logically about objects and events; achieves conservation of numbers, mass and weight; classifies objects according to several features adn can order them in series along a single dimension
4. Formal Operational: (11 +): can think logically about abstract propositions and test hypotheses systematically; Becomes concerned with the hypothetical, the future and ideological problems





Question: What is the Zone of Proximal Development (ZPD)?
Answer: - difference between what a child can perceive by them self vs what they can perceive with others
- scaffolding, guided learning
- We assess where a student is at ad then place our goal at a place that causes them to reach


Question: What is the Process of being coming a Counter?
Answer: 1. Precounter: no verbal counting skills
2. Reciter: counts using words, no one to one correspondance
3. Corresponder: can count in order, has one to one correspondance but no cardinality
4. Counter: Can count objects in organized display; have cardinality


Types of Problems

Question: Name and describe all the different types of problems. Give an example of each
Answer: Join: Result Unknown: known start and change, unknown result (3+4=?)
Join: Change Unknown: Known start and result, unknown change (3+ ?=7)
Join: Start Unknown: Known change and result, unknown start (?+4=7)
Separate: Result Unknown: Known start and change, unknown result (7-4=?)
Seperate: Change Unknown: Known Start and Result, unknown change (7-?=3)
Separate: Start Unknown: Known change and result, unknown start (?-4=3)



Question: Describe what type of problem this is: Some plums were in the basket. Four more plums were added tothe basket. Now there are nine plums. How many plums were inthe basket before more plums were added?
Answer:

Question: Lastly, Andrew tried to compute his expenses for the game night. Ifhe spent $9.00 for each game they played and they played a total of5 games, how much money did he spend that night?
Answer:

Question: Marian also baked oatmeal cookies for her classmates. If she canplace 12 cookies on a tray at a time, how many trays will she need toprepare 276 oatmeal cookies at a time?
Answer:

Question: She also decided to contribute to the collection of the Museum ofNatural History. After donating some of her bug collection, she wasleft with 39 bug species. If she originally has 98 bug species, howmany did she donate? 
Answer:

Misc.

Question: What is the problem with using key words?
Answer: - Often are no key words
- Can't use this strategy in two step problems
- Sometimes the key words can be misleading
-Encourages students to ignore the meaning of the problem


Question: What is Reflective Disposition?
Answer: - Important to make time to be self conscious and reflective
- Always more to learn


Question: What are the three main early number concepts?
Answer: 1. Relationships between #1-10: one or two more, one or two less, counting forwards and backwards
2. Benchmarks of 5 and 10: ten frames, connects to decomposition, counting by 5s and 10s
3. Part-Part-Whole Relationships: missing parts, composition and decomposition



Question: Landmark or benchmark numbers
Answer:

Question: The importance of quantity: ability to count out five blocks vs the ability to count to 5
Answer: - Knowing how to count to five can just be rote, and you do not yet have the skill of cardinality. Once you have five blocks you have the skill of cardinality and one-to-one correspondance and therefore are further along in the trajectory.