Using Student-Response Systems in Entry-Level College ... · Use the product, quotient, zero...
Transcript of Using Student-Response Systems in Entry-Level College ... · Use the product, quotient, zero...
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Using Student-Response Systems in Entry-Level College Mathematics
Courses
NCTM Regional Conference, Louisville, KY
November 7, 2013
Jonathan Engelman, MAKettering College
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Roadmap
S Formative Assessment
S What are clickers?
S One clicker sequence, with results
S Debrief
S Plethora of example questions
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What is the goal of teaching?
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The Three Questions:
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The Three Questions:
S 1. Where is the learner right now?
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The Three Questions:
S 1. Where is the learner right now?
S 2. Where is the learner going?
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The Three Questions:
S 1. Where is the learner right now?
S 2. Where is the learner going?
S 3. How will the learner get there?
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Formative Assessment Characteristics
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Formative Assessment Characteristics
S 1. Intended outcomes of learning are clearly stated and shared
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Formative Assessment Characteristics
S 1. Intended outcomes of learning are clearly stated and shared
S 2. Designed to collect quality evidence to inform teaching and improve learning
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Formative Assessment Characteristics
S 1. Intended outcomes of learning are clearly stated and shared
S 2. Designed to collect quality evidence to inform teaching and improve learning
S 3. Formative feedback to improve learning is provided to each student
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Formative Assessment Characteristics
S 1. Intended outcomes of learning are clearly stated and shared
S 2. Designed to collect quality evidence to inform teaching and improve learning
S 3. Formative feedback to improve learning is provided to each student
S 4. Students are engaged in the assessment process and, to the extent possible, in planning their own next steps for learning
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QuestioningAn Assessment for Learning Strategy
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3 Things to Take Away About Questioning
S Plan questions ahead of time
S Questions directly connect to lesson objectives
S Leave enough time for students to think, respond to the prompt, and respond to one another
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Planning Your Questions
S Previous Material/Warm Up Questions:
S Pre-Assessment Questions
S Engagement Questions
S Checking for Understanding Questions
S Wrap Up Questions
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Clickers in 30 Seconds
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Clicker Questions
S Three types:S Multiple ChoiceS NumericS Alpha Numeric
S Can be timed or un-timed
S Can be scored for correctness or participation
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Example Sequence: Exponents
S Use the product, quotient, zero exponent, negative exponent, power, and special product rules for exponents in order to simplify them.
S Use order of operations to simplify real number expressions containing exponents
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Critical Thinking Question
SSimplify:
12
(�3)2
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Critical Thinking Question
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Note
SThe following question was added after section 1 and before sections 3 and 4
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Critical Thinking Question
SSimplify:
15
�32
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Critical Thinking Question
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Critical Thinking Question
SSimplify:
17
x
7
x
�4
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Critical Thinking Question
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Critical Thinking Question
S vs SA) Both -16SB) Both 16SC) 16, -16SD) -16, 16SE) None of the above
19
�24 (�2)4
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Critical Thinking Question
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Critical Thinking Question
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Debrief
S What did you notice about this questioning strategy?
S What worked about the strategy?
S When could this strategy be useful?
S How might you implement the strategy in your class?
S http://mathquest.carroll.edu/
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Debrief: Formative Assessment
S Asking questions that point toward the goal/s for the day
S Change instruction based on results
S Class discussion: “Why is that the right answer?”
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Questioning “on the Fly”
S Wait time – first and second
S How can the prompts we developed in the first strategy help you increase your wait time?
S “what do others think?”S “how do you know if that is true or not?”S “who can add on to what Lindsay just said?”
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Pitfalls
S How much time to spend on each question?
S Cost of technology
S Multiple choice questions
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Resource
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Resource
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Resource
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Resource
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Questions?
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Bonus Questions
31
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Critical Thinking Question
SConvert 8 m to mm:SA) 0.08 mmSB) 0.8 mmSC) 80 mmSD) 800 mmSE) 8000 mm
32
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Critical Thinking Question
SConvert 7.68 kg to pounds. Round to 2 decimal placesSA) 3.48 lbSB) 3.49 lbSC) 16.90 lbSD) 16.91 lbSE) None of the above
33
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Critical Thinking Question
STrue or False: 1 is a prime number.SA) TrueSB) False
34
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Critical Thinking Question
SFind the GCF of 360 and 1350.
35
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Critical Thinking Question
SFill in the blank: -4____-(-5)SA) >SB) <SC) SD) SE) =
36
�
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Critical Thinking Question
SSimplify without using a calculator:
37
(�10 + 4) · (�3)
�7� 2
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Critical Thinking Question
SSimplify without using a calculator:
38
21
5÷ 7
15
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Critical Thinking Question
SSimplifySA) SB) SC) SD) SE)
39
p32p
322p16
16p2
4p2
2p4
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Critical Thinking Question
SSolve: -(9-3x)-(4+2x)-4=-(2-5x)-x
40
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Critical Thinking Question
S In a chemistry class, 12 liters of a 12% alcohol solution must be mixed with a 20% solution to get a 14% solution. How many liters of the 20% solution are needed?
41
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Critical Thinking Question
S The weight of an object above Earth varies inversely as the square of its distance from the center of Earth. If an astronaut in a space vehicle weights 57 pounds when 6700 miles from the center of Earth, what does the astronaut weight when 4090 miles from the center?
42
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Critical Thinking Question
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Factor: 2x
2+ x� 36
A) (2x� 4)(x+ 9)
B) (x+ 4)(2x� 9)
C) (2x+ 4)(x� 9)
D) (x� 4)(2x+ 9)
E) None of the Above
Factor: 25x
2 � 20x+ 4
A) (5x� 1)(5x� 4)
B) (5x+ 1)(5x+ 4)
C) (5x� 2)
2
D) (5x+ 2)
2
E) None of the Above
Factor: x
4 � 1
A) (x� 1)(x+ 1)(x
2+ 1)
B) (x
2 � 1)(x
2+ 1)
C) (x� 1)(x+ 1)
3
D) (x� 1)
2(x+ 1)
2
E) None of the Above
Factor: x
3 � 27
A) (x� 3)(x3)2
B) (x� 3)(x
2+ 3x+ 9)
C) (x� 3)
2(x+ 3)
D) (x� 3)(x+ 3)(x+ 9)
E) None of the Above
1
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Critical Thinking Question
SFor any value of x, the point (x,0) lies on the _____-axis.
44
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Critical Thinking Question
SFor any value of y, the point (0,y) lies on the _____-axis.
45
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Critical Thinking Question
SCalculate the slope between the points (-4,3) and (-3,4).
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Critical Thinking Question
SWrite the slope-intercept form of the equation of the line passing through (5,8) with a slope of -2.
47
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Critical Thinking Question
SFind the slope of the line perpendicular to 2x+3y=6.
48
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Critical Thinking Question
Does the graph of the function open up or down?
A) Up
D) Down
f(x) = x
2 + 2x+ 6
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Critical Thinking Question
What is the equation for the axis of symmetry for the function?
f(x) = x
2 + 2x+ 6
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Critical Thinking Question
What is the y-coordinate of the vertex of the function?
f(x) = x
2 + 2x+ 6
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Critical Thinking Question
What is the y-coordinate of the y-intercept of the function?
f(x) = x
2 + 2x+ 6
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Critical Thinking Question
What are the x-intercepts of the function?
A) x=2,3
B) x=-2,-3
C) x=-2,3
D) x=2,-3
E) No solution
f(x) = x
2 + 2x+ 6
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Critical Thinking Question
What is the domain of the function?
f(x) = x
2 + 2x+ 6
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Critical Thinking Question
What is the range of the function?
f(x) = x
2 + 2x+ 6
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Critical Thinking Question
S If $20,000 is invested at 3% annual interest, how much money, to the nearest cent, is in the account after 4 years if compounded continuously?
56
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Critical Thinking Question
S Which of the following ordered pairs is a solution to the system?
S -2x+3y=11 and -2x+2y=4S A) (-4,1)S B) (1,3)S C) (5,7)S D) (-1,3)S E) None of the above
57
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Critical Thinking Question
SFind the angle of least positive measure that is coterminal with:
58
539�
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Critical Thinking Question
SFind if .
59
csc ✓ sin ✓ =2
3
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Critical Thinking Question
SUse identities to find if with in quad. IV.
60
sec ✓ sin ✓ = �p3
2✓
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Critical Thinking Question
S Given a triangle with angles A, B, and C, and opposite sides a, b, and c, find the measurements of the remaining angle and sides assuming that B=30 degrees, C=100 degrees, and b=20 ft.S A) A=50 degrees, c=39.39 ft, a=30.64 ftS B) A=50 degrees, a=10.5 ft, c=20.26 ftS C) A=50 degrees, a=30.64 ft, c=30.64 ftS D) A=230 degrees, a=30.64 ft, c=39.39 ftS E) None of the above
61
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Critical Thinking Question
SFind the (arithmetic mean, median, mode, range, midrange, standard deviation) of the following set of data:S10,8,11,11,11,13,15
62
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Critical Thinking Question
SA coin is flipped three times in a row. What is the probability of getting 3 tails in a row?
63
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Critical Thinking Question
S If a single die is rolled, what is the probability of a 2 or an odd face coming up? Round your answer to three decimal places.
64
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Critical Thinking Question
SA jar contains 4 red spheres, 3 blue spheres, and 2 yellow spheres. Two spheres are drawn without replacement. Find the probability that a yellow sphere is drawn and then a blue ball, in that order. Round your answer to three decimal places.
65
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Critical Thinking Question
SEvaluate the expression for x=3 and y=-5.
66
x� 3y
2+ xy
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Critical Thinking Question
• Evaluate the expression:
• A)
• B)
• C)
• D)
• E) None of the above
x
�2y
3z
�4
x
�3y
5z
5
x
2/3y
3/5z
�4/5
xy
2z
9
x
�5y
8z
x
y
2z
9
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Critical Thinking Question
68
Factor: 2x
2+ x� 36
A) (2x� 4)(x+ 9)
B) (x+ 4)(2x� 9)
C) (2x+ 4)(x� 9)
D) (x� 4)(2x+ 9)
E) None of the Above
Factor: 25x
2 � 20x+ 4
A) (5x� 1)(5x� 4)
B) (5x+ 1)(5x+ 4)
C) (5x� 2)
2
D) (5x+ 2)
2
E) None of the Above
Factor: x
4 � 1
A) (x� 1)(x+ 1)(x
2+ 1)
B) (x
2 � 1)(x
2+ 1)
C) (x� 1)(x+ 1)
3
D) (x� 1)
2(x+ 1)
2
E) None of the Above
Factor: x
3 � 27
A) (x� 3)(x3)2
B) (x� 3)(x
2+ 3x+ 9)
C) (x� 3)
2(x+ 3)
D) (x� 3)(x+ 3)(x+ 9)
E) None of the Above
1
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Critical Thinking Question
69
Factor: 2x
2+ x� 36
A) (2x� 4)(x+ 9)
B) (x+ 4)(2x� 9)
C) (2x+ 4)(x� 9)
D) (x� 4)(2x+ 9)
E) None of the Above
Factor: 25x
2 � 20x+ 4
A) (5x� 1)(5x� 4)
B) (5x+ 1)(5x+ 4)
C) (5x� 2)
2
D) (5x+ 2)
2
E) None of the Above
Factor: x
4 � 1
A) (x� 1)(x+ 1)(x
2+ 1)
B) (x
2 � 1)(x
2+ 1)
C) (x� 1)(x+ 1)
3
D) (x� 1)
2(x+ 1)
2
E) None of the Above
Factor: x
3 � 27
A) (x� 3)(x3)2
B) (x� 3)(x
2+ 3x+ 9)
C) (x� 3)
2(x+ 3)
D) (x� 3)(x+ 3)(x+ 9)
E) None of the Above
1
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Critical Thinking Question
SMultiply and simplify:
70
x� 3
2x+ 4· 10x+ 20
5x� 15
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Critical Thinking Question
• Simplify:
• A)
• B)
• C)
• D)
• E)
✓x
�1/4
y
�2/3
◆�12
⇣y
x
⌘11
y
18
x
48
x
48
y
18
x
3
y
8
y
8
x
3
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Critical Thinking Question
SSimplify:
72
2 +p�4
1 + i
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Critical Thinking Question
S If (x-2)(x+1)=10, thenSA) x-2=10 or x+1=10SB) x=4 or x=-3SC) x=2 or x=-1SD) x=5 or x=-2SE) None of the above
73
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Critical Thinking Question
SSolve and check your answer:
74
p6y � 11 = 2y � 7
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CRITICAL THINKING QUESTION
Solve the inequality:
A)
B)
C)
D)
E) None of the above
4 < 2� 2x 14
�1 > x � �6
1 > x � �6
�2 > x � �12
�1 > x � �12
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Critical Thinking Question
A diameter of a circle has endpoints (4,-3) and (-2,5). What is the equation of this circle?
A)
B)
C)
D)
E) None of the above
(x� 1)2 + (y � 1)2 = 10
(x� 1)2 + (y � 1)2 = 25
(x+ 1)2 + (y + 1)2 = 100
(x� 3)2 + (y + 1)2 = 10
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Critical Thinking Question
S Are the given lines parallel, perpendicular, or neither?
S Line 1: 2x+4y=12
S Line 2: 2x-y=4S A) ParallelS B) PerpendicularS C) Neither
77
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Critical Thinking Question
STrue or false: If a and b are in the domain of f(x)=1/x, then a+b is also in the domain of f(x).SA) TrueSB) False
78
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Critical Thinking Question
True or False: The function is an odd function.
D) False
B) True
f(x) = x
3 + x+ 1
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Critical Thinking Question
STrue or False: The graph of y=f(x) and y=f(-x) cannot be the same.SA) TrueSB) False
80
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Critical Thinking Question
True or False: You get the same graph by shifting the graph of two units up, reflecting the shifted graph in the x-axis or by reflecting the graph of in the x-axis, and then shifting the reflected graph up two units.
D) True
E) False
y = x
2
y = x
2
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Critical Thinking Question
STrue or False: The functions f and g are inverses of each other:
SA) TrueSB) False
82
f(x) = g(x) =1x
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Critical Thinking Question
STrue or False:
SA) TrueSB) False
83
loga(u+ v) = loga u+ loga v
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Clicker Question
The terminal side of in standard position contains the given point. Find the exact value of .
(-3,4)
✓
csc(✓)
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Critical Thinking Question
85
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