final exam Flashcards
1
Q
What are the five strands of math proficiency?
A
- Procedural fluency
- Strategic Competence
- Adaptive reasoning
- Conceptual understanding
- Productive disposition
2
Q
What are some aspects of procedural understanding?
A
- Rules and procedures
- Short term learning
- Situation specific
- Passive learning
- Someone or something else is the source of knowledge
3
Q
What are some aspects of conceptual understanding?
A
- Meaningful ‘networks’ of information (not just rules)
- Long term learning
- Adaptable
- Actively involved
- See self as capable (develop own expertise
- Fits good with a growth mindset
- Speed isn’t everything
4
Q
What’s collective intelligence?
A
- The idea that two brains are better than one
- Children need to explain things to each other
5
Q
What is conceptual understanding?
A
Comprehension of mathematical concepts, operations, and relations
6
Q
What is procedural fluency?
A
Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
7
Q
What is strategic competence?
A
Ability to formulate, represent, and solve mathematical problems
8
Q
What’s adaptive reasoning?
A
Capacity for logical thought, reflection, explanation, and justification
9
Q
What is productive disposition?
A
Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
10
Q
What is math as a network of ideas?
A
Being in the ballpark rather than on the right path —> suggests that the learning is non linear
11
Q
What are the 7 mathematical processes
A
- Communication
- Connections
- Problem solving
- Visualization
- Mental Mathematics and Estimation
- Technology
- Reasoning
12
Q
What is the 10 criteria that makes up a rich task?
A
- Accessible and extendable
- Allows for different methods and different responses
- Learners make decisions
- Offer opportunity to identify elegant or efficient solutions
- Promotes discussion and communication
- Encourages originality and invention (allows them to pose their own questions)
- Encourages ‘what if’ and ‘what if not’ questions
- Enjoyable
- Encourages learners to develop confidence and independence as well as to become critical thinkers
- Having the potential to for revealing underlying principles or make connections between areas of mathematics
13
Q
Why would you want to do a rich task?
A
- Students are more engaged and motivated
- Students’ perseverance is enhanced
- Students’ confidence is built, the potential for understanding is maximized and difference in style and approach are addressed
- An insight into what mathematics is all about is provided for students
- Students are provided with the necessary practice to become effective, efficient, confident mathematical thinkers
14
Q
What is perceptual subitizing?
A
Instant recognition of small numbers
15
Q
What is conceptual subitizing?
A
Larger quantities; recognizing groups within the larger group
16
Q
What is the core of a pattern?
A
The shortest part of the pattern that repeats
17
Q
What is the unit of a pattern?
A
A unit is each core section within a pattern
18
Q
What is the element of a pattern?
A
An element is the individual parts (ie. shapes, numbers, objects…) within a pattern core
19
Q
What is a pattern rule?
A
An unambiguous description of the pattern
20
Q
What is a repeating pattern?
A
The core of pattern repeats predictably and unchanged
21
Q
What is an increasing pattern (growing pattern)?
A
The pattern increases by a constant or by a predictable sequence
22
Q
What is a decreasing pattern (shrinking pattern)?
A
Pattern decreases by a constant or predictable sequence
23
Q
What is a recursive pattern?
A
Each element of the pattern is defined based on a previous element or elements
24
Q
What are parallel tasks?
A
Having tasks that differ slightly but are different in difficulty
25
What's a fibirachi pattern?
Using previous parts of the sequence to continue the pattern
26
What ideas are being developed in comparison?
Comparison is developing ideas of shorter/taller, thin/thick, etc.
27
What is subtizing?
Group recognition
28
What are the five different counting principles?
- One-to-one principle
- The stable order principle
- The cardinal principle
- The abstraction process
- The order-irrelevance principle
29
What is the one-to-one principle?
There is one and only one number name for each object
30
What is the stable order principle?
There is a consistent set of counting words that never changes
31
What is the cardinal principle?
The last number spoken tells how many
32
What is the abstraction process?
It does not matter what you count; the process for counting remains the same
33
What is the order-irrelevance principle?
It does not matter in which order you count; number in the set does not change
34
What is verbal counting?
the ability to produce the standard list of counting words in order (most often just rote)
Rote counting, saying the list of words, don't understand that there is an idea behind 3 or 6
35
What is object counting?
Assigning each number name to one object
36
What is cardinality
How many? Child is able to tell how many objects in all at the end of a count
37
What is hierarchical inclusion?
1 2 3 4 5 6 7 8
The idea that all of these numbers together is 8
38
Why would we spend time looking at number relationships and activities to build them?
- It takes learners beyond just counting by ones
- Learners can see connections among numbers
- It leads to thinking strategies for estimation and mental math and basic fact strategies
- More likely that learners will look for math to make sense
39
What are benchmark numbers?
They are the cornerstone of our numeration system and help with calculation and estimation (these are numbers such as 5, 10, 25, etc.)
40
What is part-part-whole relationships?
Numbers can be explained in term of their parts (6 is 5 and 1 - 6 is 5 and 4, etc.)
41
What is assessment?
The gathering of evidence
42
What is evaluation?
Making a judgement (scoring and grading)
43
What is reporting?
Communicating judgements (report cards, interview, transcripts)
44
What are the 3 different types of assessment?
- For
- As
- Of
45
What is assessment 'for' learning?
- Feedback for students
| - Instructional decisions
46
What is assessment 'as' learning?
- Focus on developing critical thinking skills
- Metacognition for students decision making
- Focuses on the role of the student as the critical connector between assessment and learning
- Requires that teachers help students develop, practice, and become comfortable with reflection, and with a critical analysis of their own work
47
What is assessment 'of' learning?
- Summative
- Used to confirm what students know and can do, to demonstrate whether they have achieved curricular outcomes, and sometimes to show how they placed in relation to others
- Making decisions about whether students have achieved the desired outcome
- Reporting results (report cards, conferences)
48
What are the 4 different kinds of rubrics?
- Holistic
- Analytic
- Task specific
- General
49
What's a holistic rubric?
It describes qualities for each level
50
What's a analytic rubric?
It assigns scores for components of task
51
What's a task specific rubric?
A rubric specifically designed for a task
52
What's a general rubric?
A rubric that you may not have made that applies to everything
53
What is included in the introduction of the three phase lesson format?
- Make sure the expectations are clear for the during part
| - Give the students all the directions before
54
What is included in the during stage of the three phase lesson format?
- Let go
- Listen carefully
- Cautiously provide appropriate hints based on their thinking
- Provide a worthwhile activity after they're done (this should use / reinforce the skills)
55
What is included in the after stage of the three phase lesson format?
- Encourage appropriate discussion
- Summarize main ideas
- Make connections and generalizations
56
What's involved in drill?
- Simple Qs
- Answer
- Closed
- Timed (limits)
- Get the answer and move on (won't stop to figure it out)
57
What's involved in practice?
- Reasoning
- Choice
- Discover / explore
- Open (can have one answer but it's most likely to be open)
- Own pace
- Discussion
- Strategies
58
6 + 8 = 14
What is the '6' and '8'?
Addends
59
6 + 8 = 14
What is the '14'?
Sum
60
What are the two ways to look at addition?
- Joining
| - Part-part-whole
61
What is subtraction?
The difference between the number
62
14 - 8 = 6
What is the '14'?
Minuend
63
14 - 8 = 6
What is the '8'?
Subtrahend
64
What is the '6'?
Difference
65
What is the 3 different ways to look at subtraction?
- Take away or 'separation"
- Comparison
- Missing addend or 'part-part-whole'
66
3 + _ = 9 is an example of what type of subtraction?
Part-part-whole (missing addend)
67
Demonstrate pictorially take away, difference, and missing addend
pic.twitter.com/Ks44aP2LWl
68
What are the three different properties of addition and subtraction?
- The commutative property
- The associative property
- The zero property
69
What is the commutative property of addition?
You can change the order of the addends and it does not affect the answer
70
What is the associative property?
When adding three or more numbers, it does not matter whether the first pair is added first or if you start with another pair of addends
71
What is the zero property?
The idea that adding or subtracting zero doesn't make numbers bigger or smaller
72
Why would the commutative property be advantageous?
- You can see the relation between these sets of numbers
- Instead of teaching all of the addition by itself and all of the subtraction by itself you can learn that all of them are related
- Shows how the operations are inverse
- They don't have to learn these rote
73
What are the 3 learning phases for basic facts? (describe them)
- Counting (when students begin to use counting on, are ready for reasoning)
- Reasoning strategies (Using known facts to figure out unknown)
- Mastery (Use only after students known a fact and are ready to work towards accuracy)
74
What is counting on?
Being able to count on from a specific number
Instead of counting 1, 2, 3, 4....6 and then add 3; 7, 8, 9
Add 6, 7, 8, 9 instead
75
What's direct modelling?
Direct modelling physically shows the entire quantity involved in the equation
76
Name 3 examples of derived facts
- Doubles / near
- Making tens
- Making landmark / friendly numbers
- Compensation
- Breaking place value
- Adding up chunks
77
Name 5 addition strategies
- Commutativity
- Adding zero, one
- Counting on (up) 3 or less
- Doubles
- Near doubles
- 10 sums
- Near sums to 10
- Regrouping to 10 (adding 8 or 9 as one addend)
78
What are fact families?
5 + 7 = 12 --> 12 = 5 + 7
- This shows that it doesn't matter which side of the sum is on the equation
- We want kids to be flexible and have them know that they can put it in different places
79
What is foundational place value understanding built through?
- Children's early number experiences using benchmark numbers of 10
- Using 10 frames to build understanding of the 'teen' numbers (13 is one 10 and 3)
- Using 'make ten' strategies for learning the basic facts ( 9 + 6 --> 10 + 5)
- Using 10 frames and rekenreks to add / subtract
80
What are the two big ideas about place value (numeration)?
- There is a consistent trading rate from one place value to another
- Location of the digits indicated their value
81
Would one-hundred and thirty two be a correct way of saying it?
No
82
Using place value we can ________ numbers to make them easier to compute
decompose
83
Instead of 'borrow' or 'carry' what words should you use?
'trade', 'regroup' or 'exchange'
84
What are the three main kinds of base 10 blocks called?
flat (100)
rod / long (10)
unit (1)
85
Why would you want to use neutral terminology for base 10 blocks?
- **doesn't expire
| - So we can use them for different place values
86
Personal strategies are...
- Number oriented (build on place value)
- Left to right (the natural way that children work)
- Flexible (choose efficient method for numbers included)
- Students make fewer errors
- Students are 'doing' mathematics
- Faster in the long run
87
Standard algorithms are...
- Digit oriented
- Right to left
- Rigid (one strategy is used for all computations)
- Errors are often systematic and difficult to remediate
- Focus is on rules and tricks
- Students are copying, memorizing methods
- Faster only in the short run
88
Why would you learn more than one strategy?
Learning the number sense
89
Estimation helps students understand what is _____ enough
Close
90
Rounding isn't a _____ and _____ rule, you wan't them to see that it's close to a number
hard
| fast
91
What is our aim with number strategies?
The ultimate goal of number talks is for students to compute accurately, efficiently and flexibly
92
27 + 38 =
Using place value methods adding from left to right
20 + 30 = 50
7 + 8 = 15
50 + 15 = 65
93
27 + 38 =
Using adding on (counting up)
27 + 30 = 57
| 57 + 8 = 65
94
27 + 38 =
Using compensation (add an amount to make it easier, then subtract at the end)
27 + 40 = 67 (add 2)
| 67 - 2 = 65 (subtract 2)
