** Number
Concepts, Probability and Statistics **

**from****
an Advanced Standpoint (4-8) **

**Math 5370 (seminar
CRN 27852)**

WELCOME! ¡BIENVENIDOS! Tuesday, January 17, 2006

**Description**: Making connections to content, pedagogy,
technology, and assessment, this course is aligned with the two MMT areas
listed below. Topics covered will be
drawn from those listed in a way appropriately responsive to interests,
backgrounds, resource availability, logistics, scheduling/sequencing issues,
balancing depth and breadth, etc.

* __Standard I (number concepts) the arithmetic
structure of real & complex numbers__ –
basic operations in real numbers in context of real-life situations;
analysis of error patterns occurring on algorithms of the basic operations in
rational and real numbers; multiple representations of rational numbers, and
the meaning of basic operations in the context of these representations;
explore the motivation for the rules of exponents, and see how these apply to
non-rational exponents; complex numbers and how they arise naturally from
problems such as solving quadratic equations with no real roots.

* __Standard IV (concepts of probability and
statistics)__— simple probability calculations using rules such as the
addition rule and multiplication rule; simple manipulations with random
variables; various techniques of describing and analyzing univariate
and bivariate data, including appropriate use of
technology; analysis and interpretation of statistical information from media.

**Meetings**: each Tuesday (except March 14 so you can
celebrate “Pi Day”) 5-7:50pm (this window includes 20 minutes of break time,
the exact timing of which will vary in response to the flow of that evening’s
class); in Bell Hall 143 (*not* Old
Main 306). Some class lab activities
requiring technology access will use Bell Hall’s adjacent lab area.

**Instructor**: Assoc. Prof. Dr.

I began teaching university courses (especially statistics!)
in 1988, and I’ve also worked 2 years as a state agency statistician and 2
(recent) years as a full-time high school teacher & department chair! More info and resources at: **www.math.utep.edu/Faculty/lesser/**.

**Office hours: **a “final schedule” and** **changes will be announced and posted,
but my Bell Hall 213 office hours will start off including Tuesday 4:15-5 and
Wednesday 4:30-5:30. I’m usually available during intra-class “breaks”, for a
few minutes after class, by appointment, and feel free to ask questions by
phone (747-6845; “SIR-OUIJA”) or email (**Lesser
(at) utep.edu**). It’s both my job
and privilege to serve you and to offer guidance.

**Grades**: determined by the usual cutoffs of 90, 80,
70, 60, based on these parts:

22% midterm test on prob/stat (currently scheduled for March 7)

22% midterm test on number concepts (currently scheduled for April 25)

25% Projects/labs/homework/quizzes

25% Final Exam/Project: scheduled by UTEP for Tues., May 9, 2006 from 4-6:45pm

6% Class participation/attendance, which is calculated as 100(M – U – E)/M,

where M = # of class meetings we have,

U = # of days of unexcused absence/nonparticipation,

E = max{0, # of days of excused absence/nonparticipation – 2}

**Attendance**: ** is taken and required**, and is very
important considering that much of this course involves beyond-the-book group activities
or discussions that are virtually impossible to recreate on one’s own. The instructor may count tardiness or early
departure as a half-absence or even a full absence, depending on what is
missed. In general (out of fairness and
logistics), **late work will not be
accepted**, and may be subject to a penalty in the rare cases that it is
accepted. If you miss an exam without a
documented strong excuse relayed to me at the earliest opportunity, the score
will be a 0. If you miss a class, it’s **your
responsibility** to do both of these at the earliest opportunity before the
next class meeting:

(1) let me know by email (**Lesser
(at) utep.edu**) or voicemail (747-6845) or daytime math dept. fax
(747-6502) at the earliest opportunity, especially if the absence might be
“excused” or if you have a situation which may affect a test or multiple class
meetings. Give me a written note or
email by the 15^{th} day of the semester (Feb.6) if you will have
absence for religious holy days (which are excused, of course).

(2) have a classmate (pick a couple of study buddies NOW if you need to) give you copies of notes, handouts and announcements (and turn in any work).

As the UTEP *Catalog* says, “When in the judgment of the instructor, a student
has been absent to such a degree as to impair his or her status relative to
credit for the course, the instructor may drop the student from the class with
a grade of “W” before the course drop deadline [March 24] and with a grade of
“F” after the course drop deadline.” For
this class in particular, **3 or more
unexcused absences may result in an instructor-initiated drop**. A strong record of attendance will be taken
into account if your final average misses a letter grade cutoff barely (e.g.,
by less than a point).

**Professionalism**: Professional courtesy and a positive,
collaborative attitude are expected and required (this includes using
discretion regarding cell phones and beepers during class time). Be open to using/sharing opportunities for professional
growth beyond this class, such as attending and presenting at the fall 2006
GEPCTM meeting or the spring 2006 UTEP Student Research Expo. I expect to learn from you, too!

Also, while not a “requirement” of this course, start thinking now about:

(1) encouraging your students to enter the ASA Poster/Project Competition due in April:

**http://www.amstat.org/education/index.cfm?fuseaction=k12**

**http://www.amstat.org/education/index.cfm?fuseaction=poster1**

(2)
sponsoring
a mathematical project/contest/party to celebrate Pi Day in March:

**http://www.tenet.edu/tctm/downloads/TMT_Fall_04.pdf**
has an article I wrote on this

**Academic Integrity**: As
teachers, I trust that you especially appreciate how cheating, plagiarism and
collusion in dishonest activities are serious acts which erode a school’s
purpose and integrity and cheapen the learning experience for us all.
This is also particularly crucial given the ethical challenges statistics
presents to those who may be tempted to “make the numbers say what they want
them to say.” It is expected that work
you submit will represent your own effort (or your own group’s effort, if it is
a group project) and will not involve copying from or accessing unauthorized
people or resources. Violations are unacceptable and will be referred to
the Dean of Students Office for possible disciplinary action. Don’t resubmit work completed for other
classes without specific acknowledgment and permission from me.

__For Group
Work__: Within a group, members are
allowed to divide up subsets of the project for which individuals will take the
initial responsibility for coordinating efforts, but it is assumed that by the
time a group turns in a writeup that all members have
read, discussed and understand all parts of what is being turned in. Group members may even discuss general ideas
and strategies with members of other groups, but NOT share parts of actual
written work. At a minimum, to be safe,
put away all written notes and writing materials and recording devices before
having any intergroup conversations.

**Disabilities**:
If you have or believe that you have a disability that will require accommodations or modifications, you may wish
to self-identify by contacting the Disabled Student Services Office (DSSO) to
show documentation or register for testing and services. DSSO
will ask you to discuss needed accommodations with me within the first 2 weeks
of the semester [**Jan. 31**] or as soon as disability is known, and at
least 5 working days before an exam. DSSO
provides these services: note taking, sign language, interpreter, reader and/or
scribe services, priority registration, adaptive technology, diagnostic testing
for learning disabilities, assistance with learning strategies/tutoring,
alternative testing location and format, and advocacy. All information provided to DSSO is kept with
strict confidentiality. You can reach DSSO at: 747-5148 or **slopez@utep.edu** or www.utep.edu/dsso/
or go by Room 108 of the

**Textbook**: [A copy is on reserve in the UTEP

**Jessica
Utts’ Seeing Through Statistics** (3

This book (supplemented by class discussion/activities) will be the content resource for the probability/statistics component. Coming from class discussion and handouts, the number concepts topics will include:

1.) What are the number systems (and how do they arise?):

2.) Check for Properties of number systems under certain operations

(e.g., Closure Identity Inverse Commutative Associative Distributive)

3.) Multiple representations and real world examples of each type of number

4.) Conceptual/Physical Models for arithmetic operations on integers

5.) Conceptual/Physical Models for arithmetic operations on fractions

6.) Conceptual/Physical Models for arithmetic operations on complex numbers

7.) Motivating the Rules for exponents

8.) Order of operations (PEMDAS and its pitfalls), etc.

9.) Standard Arithmetic algorithms – why do they work?

10.) Analysis of alternative algorithms and error patterns in student work

**Technology**: I will facilitate in-class demonstrations or
explorations using certain manipulatives or a
graphing calculator (e.g., **TI-73**
or **TI-83**). **Please
bring an appropriate calculator to each class.** You’ll be allowed to use a calculator on many
assessments, but still have to be prepared to “show your work” so that I can
see your process and understanding and what you punched in the calculator. Simple example: if finding the mean of the numbers 1, 5, 6
you can’t just say “4”, but need to write out

(1 + 5 + 6)/3 = 4. As logistics and interest allow, we’ll also explore how statistics are computed with technology such as Web applets, spreadsheets, statistics software, etc.

**Additional Resources**:

Examples of **BOOKS**
recommended for further connections:

*Navigating through
Data Analysis in Grades 6–8 (with CD-ROM),* NCTM

*Navigating through
Probability in Grades 6–8 (with CD-ROM), *NCTM

*Teaching Statistics and Probability* (Eds: A.P. Shulte & J.R. Smart), 1981 NCTM Yearbook

*Developing Number
Sense in the Middle Grades: **Addenda Series **(Gr. 5-8)*, NCTM, 1991

*Error Patterns in Computation*
(9^{th} ed.), Robert Ashlock, Prentice-Hall,
2006

*The Best of Teaching Statistics*, 1986 (free at:

*G**etting The
Best from Teaching Statistics*,
2000 (free at:

*Mathematics Activities for Teaching and Learning* (11^{th}
ed., 2003), Barnard & Wheeler,

Kendall/Hunt.

It probably won’t surprise you
that there are also lots of free statistics textbooks, glossaries, and
calculators you can find with a **Google**
search. I have some resource links at:

**http://www.math.utep.edu/Faculty/lesser/STATResources.html**.

**In class, we’ll
explore many activities from the Teacher Quality Grant Program:**

**online.math.uh.edu/MiddleSchool/Modules/Module_5_Prob_Stat/Activities/activities1.htm** AND

**online.math.uh.edu/MiddleSchool/Modules/Module_1_Number_Operations/Activities/activities.htm**

Internet applets **http://www.shodor.org/interactivate/activities/tools.html#pro**

**http://illuminations.nctm.org/swr/list.asp?Ref=2&Std=4**

**http://illuminations.nctm.org/tools/index.aspx**)

Spreadsheets (e.g., Microsoft Excel)

**http://office.microsoft.com/en-us/FX010858001033.aspx**

**http://www.baycongroup.com/el0.htm**

**http://www.usd.edu/trio/tut/excel/**

**http://www.amstat.org/publications/jse/v4n1/nash.html**

Stats software **http://www.minitab.com/resources/tutorials/default.asp**

**http://www.keypress.com/catalog/products/software/Prod_TinkerPlots.html**

**Journals ***(the first 3 of these are free!)*

*Journal of Statistics Education ***http://www.amstat.org/publications/jse/**

*Statistics Teacher Network *(e.g., issue no. 67) **http://www.amstat.org/education/stn/**

*Statistics Education Research Journal*

**http://www.stat.auckland.ac.nz/~iase/publications.php?show=serj**

*Mathematics Teaching in the Middle School*

**http://my.nctm.org/eresources/journal_home.asp?journal_id=3**

*Teaching Statistics* **http://www.rsscse.org.uk/ts/**

**Standards and
guidelines**:

Master Mathematics Teacher(MMT) Standards:

**www.sbec.state.tx.us/SBECOnline/mtp/mmt/finalstandards.pdf**

**www.tea.state.tx.us/rules/tac/chapter111/ch111b.html**

(NCTM) Standards for School Mathematics:

**standards.nctm.org/document/index.htm**
(nonmembers can get full 90-day access *free*)

**G**uidelines
for **A**ssessment and **I**nstruction in **S**tatistics **E**ducation
Curriculum Framework:

**http://www.amstat.org/education/gaise/GAISEPreK-12.htm**