After reaching Chapter 22 (I have uploaded) from Elementary and Middle School Mathematics:
Teaching Developmentally (Van de Walle et al., 2013), discuss one of the following:
� It is understood that both experimental and theoretical probability are important, but the ways that
they support each other are less clear. What are the advantages of having students conduct
experiments even before they attempt to figure out a theoretical probability? What are the reasons for
setting up experiments with small sample sizes? How might you help students understand variability,
fair/unfair events, and the law of large numbers?
� What are some misconceptions and challenges students have with learning probability? Analyze
one of the following expanded lessons: Testing Bag Designs or Design a Fair Game. Give a brief
summary of the lesson and discuss how the activity can help students address misconceptions with
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school
mathematics: Teaching developmentally (8th ed.). Boston, MA: Pearson Education, Inc
THEORETICAL AND EXPERIMENTAL PROBABILITY 2
Students who begin their lessons of probability based on experiments rather than
theoretical provides them with an opportunity of comprehending the topic. Experiments that
are conducted in schools are based on life experiences that students can relate to. This forms
the foundation for the students to understand probability as they can visualize the various
concepts of probability (Van de Walle et al., 2013).
Also, the experiments are conducted in a fun way to make sure that the students are
intrigued throughout the unit. Moreover, using experiments as the base of teaching
probability does provide the students with problem-solving skills. The skills will be useful as
they progress to theoretical probability (Billestein et al., 2015).
The small sample size makes it easier for the experiments to be completed on time.
The class lessons have a limited time frame, and different concepts have to be covered in
each lesson. Narrowing the sample size enables the students to cover the various concepts by
the end of the learning period. Additionally, a small sample size makes it easy for the
students to formulate solutions to various problems. This provides an opportunity for students
to learn the basics of probability which they can apply as they progress in their education
(Billestein et al., 2015).
In helping the students understand fair or unfair events, one needs to remind the
students about the probability continuum. Fair events refer to having an equal chance of
occurring while unfair events refer to probability without equally likely events. Activities like
race game field, lottery machine, and dice with some sides are useful in explaining the
variability concept (Van de Walle et al., 2013).
On the other hand, on the aspect of the law of large numbers, the teacher needs to
increase the number of trials that the students are conducting in the experiments. The law of
THEORETICAL AND EXPERIMENTAL PROBABILITY 3
large numbers does state that the larger the sample the increase in the chances of the sample
mean to the mean of the entire population (Van de Walle et al., 2013). It is advisable, to
begin, with a large sample and work with the students to show them how the results get closer
The teacher can use cards where the students pull cards out of the deck. They then
record what they are pulling and return it to the deck. If the students pull a king twice in the
first four rounds, the chances of pulling a king increase to 50%. After over 20 draws and the
students have managed to pull the king twice (Billestein et al., 2015).
THEORETICAL AND EXPERIMENTAL PROBABILITY 4
Billstein, R., Libeskind, S., & Lott, J. (2015). A probability solving approach to mathematics
for elementary school teachers. and Statistics. Pearson.
Van de Walle, J. A., Karp, K.S., & Bay-Williams, J. M. (2013). Elementary and Middle School
Mathematics: Teaching developmentally (8th.ed). Boston, MA: Pearson Education Inc.