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. Larry Lesser (rhymes with “professor”, spelled like “<”)  

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: 


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)  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) 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 15th 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:

(2)   sponsoring a mathematical project/contest/party to celebrate Pi Day in March: 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 or or go by Room 108 of the East Union Building.


Textbook:  [A copy is on reserve in the UTEP Library under “Stat 1380/Lesser”]

Jessica UttsSeeing Through Statistics (3rd ed; 2005). Duxbury Press. 0-534-39402-7.

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 (9th ed.), Robert Ashlock, Prentice-Hall, 2006

The Best of Teaching Statistics, 1986 (free at:

Getting The Best from Teaching Statistics, 2000 (free at:

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



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:


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


Internet applets

Spreadsheets (e.g., Microsoft Excel)

Stats software


Journals (the first 3 of these are free!)

Journal of Statistics Education

Statistics Teacher Network (e.g., issue no. 67)

Statistics Education Research Journal

Mathematics Teaching in the Middle School

Teaching Statistics


Standards and guidelines:

Master Mathematics Teacher(MMT) Standards:

Texas Essential Knowledge and Skills(TEKS) for Middle School Mathematics:

(NCTM) Standards for School Mathematics: (nonmembers can get full 90-day access free)

Guidelines for Assessment and Instruction in Statistics Education Curriculum Framework: