The document provides instructions for an icebreaker activity involving age guessing. Students are split into groups and each group is given 10 pictures of individuals. They must guess the age of each person and record their guesses. The actual ages will then be revealed so groups can calculate their error for each guess. The group with the lowest total error will win. Statistical concepts like bias, variance, and averages are introduced through this activity.

1. Ice Breakers and Orientation

2.  My name is Jason
 Now, please get into your groups so that we
can begin our first activity

3.  In your group, look at the picture you receive
and decide, as a group, what the age of the
person in the picture is.
 Write this guess down next to the Person
Number that is on the picture, in the shaded
‘Your Guess’ column (this is your group’s
guess).
 Pass your picture on, and take another.
 Please do this for all ten pictures.
 Let’s see which group can get the lowest
error!

4.  How close do you think you are?
◦ Typically, students feel fairly confident that they
can guess within 5 years of a person’s age.

5.  I will reveal the age of each person in the
pictures.
 Write down the ‘actual age’ in the next
column.
 Please just write down the numbers now and
we’ll work on the next part together.
 Ready…
 Set…

16.  Error = Your Guess – Actual Age
◦ The error will be a negative number if your guess
was too low.
◦ The error will be a positive number if your guess
was too high.

17.  Absolute Error is the Absolute Value of the
Error
◦ If your Error was a positive number, then just write
the same number here.
◦ If your Error was a negative number, then just write
the number without the negative sign.
 All answers in this column should be positive.

18.  The Mean is one type of Average (the other
two being Median and Mode).
◦ You probably remember it better as the Weighted
Average.
◦ Find the Mean by adding up all of the data values,
and then dividing by the number of data values.

19. Person Group A Group B Group C Group D Group E Group F Group G Group H
1 75 74 70 85 82 85 84 91
2 16 17 20 18 27 23 19 17
3 65 52 55 64 68 65 73 50
4 30 26 28 27 25 27 22 25
5 27 20 17 21 23 30 25 20
6 44 43 35 48 44 40 55 43
7 80 65 75 79 86 90 85 83
8 4 3 5 6 4 4 3 4
9 53 47 45 46 58 56 58 61
10 60 51 60 56 77 66 70 70
Mean -2.9 -8.5 -7.3 -3.5 1.1 0.3 1.1 -1.9
One person from each group needs to come
to the front and fill in the data so we can all
have it

20.  Rich in statistical ideas
◦ We will return to it repeatedly during the term.
◦ Please keep the data.
◦ Concepts touch upon:
 Bias
 Variance
 Experimental Design
 Confidence Intervals

21. ADVICE TO HELP
IMPROVE
STUDYING,
LEARNING, AND
UNDERSTANDING
From “Improving Learning by
Understanding the Psychology of
Human Memory”, (Saikali, 2013),
presented at the 2013 Annual Autumn
Conference of California Mathematics
Council Community Colleges (CMC3)

22. BE PREPARED FOR THE
COURSE
 You should have all necessary items, such as:
• Books
• All recommended or required supplies
 Further, you should be sure you are capable of any skills
necessary for the class, such as:
• Computer skills
• Time to study
*

23. DO NOT OVERLOAD
YOURSELF
 Students have many responsibilities.
• Work, School, Family obligations.
• These collective demands cause their grades to suffer so that
they accumulate a poor academic record.
• They may then drop out of school, take on long-term
responsibilities, and regret forever that they did not go further with
their education.
• Determine how much YOU can handle and be careful about
exceeding it.
*

24. DO NOT OVERLOAD
YOURSELF
 Some commitments are inflexible.
 Perhaps the stress of other responsibilities can be moderated
with help from family members.
 Still others may be possible to reduce or remove from your life.
• Are you working many hours due to necessity or luxury?
• Could you scale back expenses, work fewer hours weekly, and still
survive financially?
• Alternatively, taking fewer units of classes per term may mean a
longer total time to graduate, but may allow you more time to study,
get sufficient rest, and hence, achieve a better academic record.
*

25. RESIST OVER-CONFIDENCE
 Usually, the first part of any course is its easiest.
 Even so, there may be bits of knowledge that you need to master.
 Moreover, when the new material comes, you need to be ready for
its challenges.
 An over-confident attitude may serve only to get you behind.
 It can be scary and frustrating to find that you are unable to keep up
with the new material in a course.
 Cramming to then retain too much material in a short time rarely
works out for students.
*

26. COME TO EACH SESSION OF A
CLASS ON TIME AND PREPARED
 In order to make best use of your time in class, you should
• complete homework exercises from previous sections;
• bring the homework with you to class;
• review the last lecture;
• read the portion of the textbook to be covered in the coming
lecture.
• This will expose you to terminology, concepts, graphs, and
methods that you may hear again in lecture.
 All of these are important efforts toward learning, studying,
and long-term remembering.

27. EXERCISE GOOD CLASSROOM
COMPORTMENT

28. EXERCISE GOOD CLASSROOM
COMPORTMENT
 Choose a seat where you can stay focused.
 Try to focus on the material and not become distracted by frivolous
things (Facebook/socializing when you should be taking notes ore staying
involved in the lecture.)
 Be attentive to the lecture, discussion, or other class activity.
 Taking good notes (and actually using them when studying) is important.
• Simply copying the board/screen content to your notebook is not much
better than photocopying someone else’s notes.
• Instead, think about what you are hearing and seeing from the speaker
as you write it.
• Writing actually does help connect material in our brains.

29. EXERCISE GOOD CLASSROOM
COMPORTMENT
 Instead, think about what you are hearing and seeing from
the speaker as you write it.
• How does it pertain to the overall theme of the lecture.
• How does it relate to what you knew before the current lecture?
• How does it relate to what you read in the textbook before
coming to class?
• If you are following all of this advice, and something you hear
or see from the speaker is unclear, raise your hand and ask for
clarification.

30. ELABORATIVE REHEARSAL IS CRUCIAL
TO LONG-TERM MEMORY RETENTION
 You can supplement in-class attentiveness by reviewing and audibly
pondering the deeper meanings of what you heard in lecture.
 Arrange a small study group in which people take turns explaining portions of
the material to the group and resolving any confusion.
 Flashcards can also serve effectively as rehearsal.
 Re-writing your lecture notes while explaining (aloud or to a friend) each part
works well for some students.
 The more you reinforce and reach a level of comfort in talking about the
lecture content, the easier it will be to remember and use what you have learned
when tested.

31. INSERT MEMORY LADDER

32. INSERT MEMORY LADDER

33. INSERT MEMORY LADDER

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46. START EACH HOMEWORK ASSIGNMENT
AS SOON AS POSSIBLE AFTER ITS
LECTURE
 Unless you quickly and often use what you hear in the
classroom and read in the textbook, you begin forgetting new
material rather quickly.
 Avoid waiting until the weekend to do multiple lectures
worth of homework.
• The amount of work can feel insurmountable and leave you
getting much less out of the exercises than otherwise possible.

48. START EACH HOMEWORK ASSIGNMENT
AS SOON AS POSSIBLE AFTER ITS
LECTURE
 As psychologist Ebbinghaus found a century ago, we begin
forgetting brand new material almost immediately
• if it is not used in meaningful ways,
• and if we do not relate it to our existing knowledge.
 Look up the Ebbinghaus Forgetting Curve online, print it
up, and carry it with you to help encourage you to start
homework ASAP!!!

49. DO HOMEWORK IN A
DISTRACTION-FREE SETTING
 Put away devices that draw focus from your work.
• Do you listen to music when you work out, or when you do
household chores? Why?
• Likely to help the time go by while you are doing something you find
boring.
• Is this really conducive to studying, learning, and remembering?
• If you are checking your telephone, social media sites, email, texts,
every few minutes, think of how little substantive attention is being
paid to what you are supposed to be learning.
• How can you reasonably expect to remember later?
• Make a printed weekly schedule of when to do homework for each
course.
• Carry it with you daily and commit to it.

50. DO HOMEWORK IN A
DISTRACTION-FREE SETTING
 Put away devices that draw focus from your work.
• Do you listen to music when you work out, or when you do
household chores? Why?
• Likely to help the time go by while you are doing something you find
boring.
• Is this really conducive to studying, learning, and remembering?
• If you are checking your telephone, social media sites, email, texts,
every few minutes, think of how little substantive attention is being
paid to what you are supposed to be learning.
• How can you reasonably expect to remember later?
• Make a printed weekly schedule of when to do homework for each
course.
• Carry it with you daily and commit to it.

51. DO HOMEWORK
RESPONSIBLY
 Start homework by reviewing the new ideas and methods (from
the lecture notes and textbook) relevant to the current homework.
• How does this new content relate to what you learned in earlier
lectures, sections of the textbook, and homework?
• Homework should strengthen the learning of new content.
• This benefit comes only if you are consistently responsible with it.
• Example problems show how to make use of a section’s material.
• It may be tempting to “do” each homework problem by looking for an
example problem to emulate without really seeking to understand the
relevant theory.

52. DO HOMEWORK
RESPONSIBLY
 Example problems show how to make use of a section’s
material.
• It may be tempting to “do” each homework problem by looking for
an example problem to emulate without really seeking to
understand the relevant theory.
• Any short-term gain from this practice will be of minimal value during a
test when no aids are available.
 For each homework problem, write the instructions and problem
statement, and show work neatly.
 When helpful, construct a table or sketch.

53. DO HOMEWORK
RESPONSIBLY
 If the problem is a True/False or Yes/No type, justify your
answer.
• That is, for example, state WHY it is true or WHY it is false.
• You can also state what would make it true if it is false.
 These practices will make studying for tests much easier, as
you should be able to remember your past work better.

54. LEARNING IS MORE IMPORTANT THAN
GETTING THE CORRECT ANSWER
 In a career occupation, you will encounter difficult problems
that take time to work through.
• If a solution approach to a homework problem does not
instantly come to you, do not rush to give up.
• Homework is supposed to be challenging.
• What would be the objective if all problems had easy-to-find
solutions?

55. LEARNING IS MORE IMPORTANT THAN
GETTING THE CORRECT ANSWER
• Before rushing to look in the book, your notes, or elsewhere for
a quick answer, stop and think.
• Are you clear on what you were being asked to do and how what is
unknown relates to given information?
• How might you use previously learned content to reason on the
current problem?
• What role do the components of a problem play in affecting the
whole?

56. LEARNING IS MORE IMPORTANT THAN
GETTING THE CORRECT ANSWER
• In the world outside of a classroom, there is no answer set in
the back of the textbook.
• There are no solutions manuals.
• You may have access to supervisors and colleagues at a job,
• but if you frequently rush to get help from those sources
rather than demonstrating that you can work on your own to
solve your problems…
• …your value to the organization will be lessened.

57. STOP AND ASK YOURSELF, “WHAT HAVE
I LEARNED?” FROM HOMEWORK
 When you complete a subset of related homework problems, take a few
minutes to consider what you have gained
• What do you know now that you did not know before?
• Could you teach it to others?
• Are you able to use what you have acquired to do other problems in this
or future sets?
 Be honest with yourself
• If you have not learned much from doing the homework, that must be
addressed.
• Telling yourself that everything will work itself out is not the remedy.
• While there are academic things that take time to mentally digest, it
should not be that way generally with your work.

58. STOP AND ASK YOURSELF, “WHAT HAVE
I LEARNED?” FROM HOMEWORK
 Be honest with yourself
• Meet with your instructor about this to get advice on what
might be wrong.
• Mathematics courses tend to follow a path of connected
learning from one section/chapter to the next.
• It is important to apply yourself well enough to use and
remember what was learned from earlier sections, or else how
can you expect to successfully move forward?

59. STOP AND ASK YOURSELF, “WHAT HAVE
I LEARNED?” FROM HOMEWORK
 Learning is sometimes very difficult and frustrating.
• The discomfort you feel, the frustration, that is the brain actually
physically rewiring itself to be better at the task at hand.
• This is one of the major reasons why learning math is such a
difficult process – the brain has to physically undergo change.
• This, combined with the fact that we are programmed to hate the
feeling of being ‘wrong’ are two major reasons why many students
‘hate’ mathematics…
• It’s not easy, it takes practice, and it takes getting things wrong many
times to learn how to get them right!
 Tell yourself that it’s OK to be wrong, it’s OK to make mistakes,
and it’s OK to feel frustrated – this is how we LEARN!!!

60. INSTRUCTOR OFFICE HOURS
 A misunderstanding of current material will interfere with you correctly
learning and remembering new material.
• It’s not ‘Practice makes perfect’ but rather…
• ‘Perfect Practice makes perfect.’
 Do you make use of your instructors office hours?
• You can and should also ask questions in class when they come up!
 When doing so, be prepared to specify what you do understand and show
that you have made reasonable effort on your own at figuring out what is
unclear.
• However, if you are truly stuck, go in and see them also!

61. WHEN PREPARING FOR A TEST, SPEND
MINIMAL TIME STUDYING WHAT YOU
ALREADY KNOW WELL
 A mistake of studying is spending too much time reviewing
what you already understand.
• This is an unproductive psychological avoidance technique.
• Notice the emphasis on ‘too much.’
• Reviewing is important, but too much is wasteful.
• Rather, devote your time to mastering material that troubles you.
 One technique to studying for a test is to create your own
realistic test and take it.
• Realistic = choose problems that aren’t too easy nor too difficult.

62. FAMILIARITY ≠ COMPREHENSION
 While there is value in rereading your lecture notes and the
textbook, do not get deluded into thinking that visual familiarity
equals understanding/retention.
• Just because something is easier to read does not mean that you are
able to reason on it to solve problems as may very well be required
during a test.
• “It was so easy when I watched YOU do it at the board, but when I got
home…”
• Also, this kind of narrow familiarity tends to not work well when a
person is presented with the same material from a different
perspective.

63. SPEND SUFFICIENT TIME STUDYING
EARLY, AND SPACE OUT STUDY
SESSIONS
 It takes time to get knowledge into your long term memory
in a way that makes it easily retrievable in the future.
• Avoid waiting until a day or two before a test to start preparing.
• Cramming is generally not as effective as people assume.
• Consistently studying daily is more conducive to retention.
• Math is a language…

64. SHORT BREAKS DURING
STUDYING
 Getting distracted every few minutes is an extreme.
 Working many hours without breaks is an extreme.
 Find a good place in between.
 Check yourself along the way to see if you are remembering
what you have studied and can demonstrate mastery of it without
peeking at notes, books, or answers.
 If comprehension is minimal, your manner of studying is
impractical.

65. SHORT BREAKS DURING
STUDYING
 Try to get up and have 5-10 minutes of physical activity for
every hour of study.
 Whenever possible, do not go longer than an 1 to 1 ½ hours
of studying without a physical activity break.
 Good nutrition and rest are also important.
• Naps, when possible, are GREAT!

66. ANTICIPATE TEST
QUESTIONS
 If you are regularly in class, taking copious notes, participating,
and responsibly doing the homework, then it could be valuable to
spend some time speculating on the possible test questions.
• Think about the content that the professor emphasized.
• Can you explain it to others?
• Are you ready to be tested on it?
• Could you make practical use of it extemporaneously?
• Do not make the mistake of assuming that everything will work
itself out during a test.
• If necessary get clarity ahead of time.
• Be clear on what content you are expected to know for a particular test.

67. IF YOU USE A TUTOR, DO SO
CAUTIOUSLY
 There is nothing wrong with consulting a tutor (in fact, it is
encouraged!) but be careful.
• Too often, help from a tutor turns into the tutor doing the
student’s work.
• How can you expect what you need to know to enter your long-
term memory and be retrievable during tests if you cannot do
much without the tutor’s help?
• A tutor should not be a substitute for working on your own.
• Is the tutor guiding you in a way that gets you to a point of
being able to function independently?
• If not, discuss this with your tutor.

68. FINAL ADVICE FOR TESTS
 Start studying well in advance of a test.
 Cramming and all-nighters are risky.
 Get enough sleep the night before a test.
 Eat properly so that you are alert and nourished.
 Gather all necessary tools (pencils, eraser, fresh batteries for your calculator, etc.)
well in advance of the test date.
 If possible, arrive to the testing site early so that you are less stressed.
 Keep a positive attitude even if the subject matter is not one you are fond of.
 These will promote your capacity to learn, remember, and do well academically.

69.  Be prepared
 Don’t take on too much
 Hit the ground running
 Come to each class, on
time, and prepared
 Use classroom time wisely
 Practice well, and a lot
RECAP OF IMPORTANT
POINTS
 Get started on homework
as soon as physically possible
after class
 Do homework in a
distraction free setting
 Do homework responsibly

70.  Learning is as important as
getting the right answer
 Ask yourself “What have I
learned from homework?”
 Utilize office hours
 Focus on trouble spots
when prepping for a test.
RECAP OF IMPORTANT
POINTS
 Familiarity ≠ Comprehension
 Study early, for sufficient
amounts of time, and often
 Physical breaks when
studying
 Anticipate test questions
 Use a tutor, but wisely

71.  Jason Edington
◦ Apparently I used to
work in radio?
 Grew up in LA
area…
◦ Went to Jr. High
with…

72.  Jason Edington
◦ Apparently I used to
work in radio?
 Grew up in LA
area…
◦ Went to Jr. High
with…

73.  Jason Edington
◦ Apparently I used to
work in radio?
 Grew up in LA
area…
◦ Went to Jr. High
with…

74. ◦ What are my hobbies?

75.  There are two major features to my teaching that I am going to utilize in class.
◦ First: I work to motivate students to embrace their education.
 I encourage students:
 to come to every class
 be prepared for class
 do the Homework
 read ahead
 Attend study groups
 You may need to take the initiative and create one!
 Come for help as SOON as you start getting behind (or heck, even before!)

76.  There are two major features to my teaching that I am going to
utilize in class.
◦ Second: Consistently remind students to be OK with struggling.
 This is a safe environment to take a chance and be wrong.
 Only by trying, and struggling, can we really succeed and grow to our full potential.
 Because we are ALL in the same class together, we need to support each other through this!

77.  Motivation, Not IQ, Matters Most for Learning New
Math Skills
◦ Time Magazine – December 26, 2012
 “Students with high IQ have high math achievement and
students with low IQ have low math achievement. But IQ does
not predict any growth in math achievement. It determines the
starting point.”
 i.e. it’s not how smart you are…

78.  Motivation, Not IQ, Matters Most for Learning New Math Skills
◦ Time Magazine – December 26, 2012
 “It’s not how smart we are; it’s how motivated we are and how effectively we study
that determines growth in math achievement over time…”
 So students who improved in math over the years were disproportionately those who
said they “agreed” or “strongly agreed” with statements such as,
 “When doing math, the harder I try, the better I perform,” or
 “I invest a lot of effort in math, because I am interested in the subject”
 This was true even if they had not started out as high-achieving students.

79.  US Math Achievement: How Bad is it?
◦ Three eye-opening studies paint a sobering picture but may point to a solution.
 Nate Kornell, Ph.D, Psychology Today, November 27, 2012
◦ Studies examined community college students who placed into remedial math class.
 The most interesting thing about the new research is that students were not tested using
traditional measures of mathematical ability.
 Sample questions:
 Students were shown a number line from -2 to 2 and asked to draw a line marking the
approximate location of two numbers: -0.7 and 13/8.
 Percentage who answered correctly: 21%

80.  US Math Achievement: How Bad is it?
◦ Three eye-opening studies paint a sobering picture but may point to a solution.
 Nate Kornell, Ph.D, Psychology Today, November 27, 2012
◦ Studies examined community college students who placed into remedial math class.
 The most interesting thing about the new research is that students were not tested using
traditional measures of mathematical ability.
 Sample questions:
 Students were asked “If a is a positive whole number, which is greater: a/5 or a/8?” Fifty
percent would answer correctly if they just guessed.
 Percentage who answered correctly: 53%

81.  US Math Achievement: How Bad is it?
◦ Math as rules versus math as a system
 “Math is just all these steps.”
 “In math, sometimes you have to just accept that that’s the way it is and there’s no
reason behind it.”
 “I don’t think [being good at math] has anything to do with reasoning. It’s all
memorization”
 77% of the students seemed to believe that math was not something that could be figured
out, or that made sense.
 It was just a set of procedures and rules to be memorized.
 This is, of course, exactly the opposite of true.

82.  US Math Achievement: How Bad is it?
◦ What is the solution that is coming out of this?
◦ The TIMSS study (Trends in International Mathematics and Science Study)
 1995
 Grades 4, 8, final year of H.S.
 U.S. vs. World: 12th < 8th < 4th
 Key differences in how teaching happens have been being looked at for
almost 20 years.

83.  US Math Achievement: How Bad is it?
◦ What is the solution that is coming out of this?
◦ The U.S. is an Outlier (as was Australia, the only other low-performing nation in the
study) when compared to some key differences in the classroom.
 Lecturing vs. Group Work
 NOT a predictive variable of success.
 Abstract vs. Real-World Problems
 NOT a predictive variable of success.
◦ So…what were the two features of instruction that predicted good math
outcomes??????

84.  US Math Achievement: How Bad is it?
◦ What is the solution that is coming out of this?
◦ So…what were the two features of instruction that predicted good
math outcomes??????
 Being explicit about the conceptual structure, and interconnectedness,
of mathematics.
 Allowing students to struggle to understand concepts.

85.  Being explicit about the conceptual structure, and interconnectedness, of mathematics.
◦ This is something that we will strive for, every day, in every aspect of our discussion, reading, and studying.
 Specifically in this class, I will point out how the concepts that you’ve been learning in Algebra and Trig will be used
in Calculus.
 Allowing students to struggle to understand concepts.
◦ This does NOT mean that I will throw you out into the wild on your own.
◦ Rather, it means that I will show you the basic ideas necessary to understand the harder problems, and you
will do the work in putting them together.
 (In other words, I’ll show you some examples, but for effective learning to take place, you WILL struggle with
problems. )
 HINT: The struggle is when the learning happens!

86.  There are two major features to my teaching that I am going to utilize in class.
◦ Again…
 Be motivated to do what it takes to learn the material.
 Be OK with struggling.
◦ Your success is the most important thing to me, and is why I teach.
◦ However, like a Sherpa, I can only show you the way…
 you have to do the climbing…

87.  Now, let’s hear about you!
◦ Please tell us the following:
 Name
 Major
 Something interesting about yourself

88.  Last Name, First Name
 Email Address
 Last class you took, and when? (Semester/Year)
 Major
 School you plan to transfer to
 Date you will graduate with your final degree
(Certificate, AA/S, BA/S, MA/S, or PhD)