Subject: Re: How Should We *Motivate* Students in Intro Stat?

     To: EdStat-L Statistics Education Discussion List, Usenet Newsgroup

   From: Donald B. Macnaughton <>

   Date: Wednesday May 7, 1997

     cc: Samuel M. Scheiner <>

Referring to an earlier post of mine (1997a), Sam Scheiner (1997) 

> While I agree in principle with almost all that Don said, I
> have a problem at the practical level.  I have attempted to
> teach these deep connections.  Frankly, most of my students
> just do not get it.  They are not stupid.  But, their past
> schooling has been so non-conceptual that it is a struggle 
> just to get them to make the simplest conceptual connections
> between ideas within narrow disciplines, much less the very
> broad ones that Don is talking about.

Sam makes an important point:  Although the ideas of entities, 
properties, and relationships have broad unifying power, the 
ideas are *useless* in the introductory statistics course if we 
cannot convey them to students.


However, it is clear that we *can* convey the ideas to students 
- we teach the ideas carefully and 
- we devote *enough class time* to the ideas.  

How much class time is needed to ensure that students master the 

My experience with the ideas in three statistics courses (1996a, 
sec. 5) suggests that well-motivated students can properly under-
stand the ideas after they have had two or three class discussion 
sessions devoted to the ideas and after they have completed re-
lated homework exercises.  Weaker students or students who are 
inexperienced in abstract thinking may need as many as four or 
five class sessions and related exercises.  Advanced students may 
master the ideas in as little as one class session or solely 
through reading.


Although it seems clear that we *can* successfully convey the 
ideas of entities, properties, and relationships to students, an 
important question remains:  Is it *worth* taking between one and 
five class sessions at the beginning of an introductory statis-
tics course to cover this new set of ideas, or will students be 
better served if we spend the time on other ideas?

Consider three points I have made in earlier essays

- The ideas of entities, properties of entities, and relation-
  ships between properties of entities serve as a broad and deep 
  foundation for most (all?) other statistical concepts and pro-
  cedures (1996a, sec 4.1).

- The ideas subsume certain important aspects of the scientific 
  method (1997a).

- The ideas mirror the way that most people think (1996a, sec 3).

These points suggest that the ideas of entities, properties, and 
relationships are important.

Consider our task of building a clear conceptual model of the 
field of statistics in students' minds.  The most *logical* way 
to develop this model is 
- start with the foundational ideas and then 
- build the other statistical ideas atop the foundational ideas.  

It is especially logical to start with the foundational ideas if 
these ideas are easy for students to understand.  Fortunately, 
the ideas of entities, properties, and relationships *are* easy 
to understand, because (a) there are only three main ideas and 
(b) the ideas mirror the way that most people think.

Since students are more likely to understand the derived ideas 
and procedures of statistics if we teach the easy-to-understand 
foundational ideas first, it is worth taking the time to convey 
the important ideas of entities, properties, and relationships to 
students at the beginning of the introductory statistics course.


I suggest five guidelines to help convey the ideas to students
- divide and conquer
- exemplify 
- maintain focus on the unifying ideas
- elicit and monitor student feedback
- use pedagogical aids.

By "divide and conquer" I mean we must first break the ideas into 
a carefully thought-out logical chain of ideas.  Then we must 
concentrate on each idea in the chain in turn until we are sure 
students understand that idea.  Experience (including Sam's expe-
rience) suggests that it may take longer than first expected to 
properly cover an idea.  

By "exemplify" I mean we must discuss each idea in terms of mul-
tiple *practical* examples.  There is a strong relationship be-
tween the number of carefully chosen examples we use to illus-
trate an idea and the degree of understanding students obtain of 
the idea.  I will discuss examples further in a later post.

By "maintain focus on the unifying ideas" I mean we must focus on 
the ideas of entities, properties, and relationships in *all* our 
discussions in the introductory course rather than taking a dif-
ferent point of view for each new statistical topic.  The power 
of the three ideas comes from their ability to unify statistical 
topics.  But the unification can only take place if we keep the 
ideas as a centerpiece of the discussion.  In particular, if (as 
is usually the case) an empirical research project can be 
*reasonably* interpreted in terms of the schema I proposed in an 
earlier post (1997b) then, to help build a single comprehensive 
model of the use of statistics in empirical research, the re-
search project *should* be interpreted in terms of the schema.  

By "elicit and monitor student feedback" I mean we must fre-
quently check the students' understanding of the ideas.  Since 
most statistical ideas are built atop more fundamental ideas, if 
the students do not first understand the fundamental ideas, there 
is *no way* they can understand the derived ideas.  Therefore, if 
our courses are to be successful, we must frequently use feedback 
systems to identify when students do not understand so that we 
can take remedial steps.  Following are some effective ways to 
elicit student feedback:
- minute papers (Mosteller 1988)
- quizzes and exercises that test students' understanding of the 
  ideas (I give examples in Macnaughton 1996b)
- two-way discussions between the teacher and students about the 

By "use pedagogical aids" I mean we should judiciously use the 
effective modern teaching techniques of 
- active learning
- group learning
- improved motivational approaches
- improved student and course assessment approaches
- computers as teaching and communication aids.
All the above techniques can be used in conjunction with an en-
tity-property-relationship approach in an introductory course.  
The value of effective pedagogical aids cannot be overestimated.

Since the entity-property-relationship approach provides a new 
point of view of the introductory course, teachers using the ap-
proach must experiment with how they present the ideas to find 
their personal best teaching strategy.  I introduce one way of 
presenting the ideas to students in a paper for students (1996b).  


I believe that if we carefully build the field of statistics atop 
the unifying foundational ideas of entities, properties, and re-
lationships, we can move our field from being the "worst course 
taken in college" to its rightful role as a respected cornerstone 
of almost all empirical (scientific) research.

Donald B. Macnaughton   MatStat Research Consulting Inc.      Toronto, Canada


Macnaughton, D. B. (1996a), "The Introductory Statistics Course:  
  A New Approach."  Available at

Macnaughton, D. B. (1996b), "The Entity-Property-Relationship Ap-
  proach to Statistics: An Introduction for Students."  Available 

Macnaughton, D. B. (1997a), "Response to Comments by John R. 
  Vokey."  Posted to the Usenet newsgroup on April 
  6, 1997 under the title "Re: How Should We *Motivate* Students 
  in Intro Stat?" Available at

Macnaughton, D. B. (1997b), "Response to Comments by Samuel M. 
  Scheiner."  Posted to the Usenet newsgroup on 
  February 24, 1997 under the title "Re: How Should We *Motivate* 
  Students in Intro Stat?" Available at

Mosteller, F. (1988), "Broadening the Scope of Statistics and 
  Statistical Education," _The American Statistician,_ 42, 93-99.

Scheiner, S. M. (1997), "Re: How Should We *Motivate* Students in 
  Intro Stat?" Posted to the Usenet newsgroup on    
  April 7, 1997.  Should soon be available at 
  (search for "How Should We" without the quotes).  Also 
  available at  Use Power Search to
  search the appropriate date range database using "~g and motivate intro stat" without the quotes.

Home Page for the Entity-Property-Relationship Approach to Introductory Statistics