Assessment Task Three
Name: Georgina Hession
Student Number: S00125386
Tutorial: 2pm Friday
Tutor: Julie
Gaining insights from research for classroom planning
Introduction (144 words)
Probabilistic reasoning is used throughout everyday life, from creating weather forecasts, to
gambling at the racetrack, to making decisions on situations in a court of law (Barnes, 1998).
According to McMillen (2008), “understanding probability and using it appropriately are necessary
skills for functioning as an informed citizen”. Evidently, probability has a very important role to
play in a student’s mathematical education. However although this is the case, many students find
probability a difficult topic to grasp due to the deep preconceived beliefs coming from experiences
that are usually inaccurately observed (Barnes, 1998). It is essential for teachers to have a deep and
full understanding on probability, complete with the knowledge of common misconceptions had by
students on the topic, as well as the skills and strategies to successfully correct these fallacies
(Edwards and Hensien, 2000). Probability is an important mathematical focus in the curriculum.
Literature review (1040 words)
Ultimately, probability is about how likely an event is of occurring (Van de Walle, Karp and Bay
Williams, 2003). Concepts such as fractions and percentages, ratios and proportions as well as data
analysis, support and form the foundations for probability. To have a clear understanding of
probability one must be able to think in the numerical form of chance, that is through fractions and
percentages (Edwards and Hensien, 2000). Students need to understand that there are three ways in
which people think of probability: Subjective Probability, which is the belief in of something
happening; Experimental Probability, which uses the frequency of an event occurring using
identical trials; and Theoretical Probability, which uses random experiments, based on theoretical
analysis (Barnes, 1998). An understanding of sample space and sample size as well as proportional
reasoning and fairness are also necessary for a true grasp on probability.
The previous knowledge students have when it comes to their overall understanding of probability
is that in relation to subjective probabilities. Students use their own beliefs of something happening
from either using their personal judgement or experience with no formal calculation (Barnes, 1998).
According to Fischbein (1975), “our intuitive ideas about probability and other mathematical
concepts are based on everyday experience and often mislead us during formal learning”. Due to
this, many students struggle with the concept of probability and chance.
A common misconception that students have is the notion of a “loaded dice”, that is that certain
numbers are “easier” to get than others. For example, the particular belief associated with the
loaded die is that throwing a six is a lot “harder” to throw compared to any other number on the
dice. This may be due to student’s experience of playing particular games with desired numbers
(Nicolson, 2005).
Another common misconception students have while studying probability is how likely something
is of happening depending solely on it’s frequency. For example, flipping a coin has a equal chance
on landing on head or tails, however in a collection of ten samples the coin may land on heads eight
times, having students believe that heads will always be the winner (Barnes, 1998).
Similarly, students believe in frequency having an impact on the following result or results. For
example believing that a run of bad luck has to eventually end and change to good luck (Barnes,
1998). Students also struggle in relation to how the sample size can affect the variability of the
proportion, that a large sample of data will hold the same variability as a small sample.
Relatedly, students also have misunderstandings about how random samples can reflect the
diversity of the population from which it is taken. Other misconceptions that students may have in
relation to probability are equal chance being mistaken for fifty/fifty or “half chance” and that
spinners with non-contiguous segments produce difference chances than spinners that have
segments of the same area next to one another (Edwards & Hensien, 2000; Nicolson, 2005). In
order for students to be able to confront these misconceptions, teachers must be aware of the
strategies used to address them.
“The critical person in any learning environment is the teacher” (Jones, 2005).
Teachers own mathematical knowledge plays a significant role in educating students on probability.
According to Jones (2005), if teachers have a poor understanding of probability along with their
own misconceptions on the subject, it will be harder for them to recognise their student’s fallacies.
This can also affect a teacher’s confidence on the subject and can ultimately disturb the educational
outcome for students. Coffey and Richardson (2005) state that teachers need to be “reflective
practitioners” when educating students on probability. Teachers need to constantly be assessing and
monitoring students understanding, so they are able to design lessons that help students build
knowledge as well as address any misconceptions (Jones, 2005). An awareness of what students
believe can assist the teacher on creating activities that address the fallacies being had and enable
students to become clear in their understandings. Teachers need to be aware of the knowledge their
students have, and how to develop it through the use of activities. They need to be able to
incorporate appropriate forms of assessment into their lessons and be able to successfully record
this (Jones, 2005).
For teachers to avoid common probability misconceptions with their students, activities that follow
a mathematical investigation process where students research, collect data, collaborate with peers
and use multiple strategies to solve problems are extremely beneficial (McMillen, 2008). Through
such an exploration, any preconceived misunderstandings that children bring with them to the
activity has the opportunity to be confronted, as students use their reasoning skills to assess their
strategies and form conclusions.
These mathematical investigations should be multidimensional in content, open ended with many
solutions, centred on a theme and should go the length of an entire class or longer (McMillen,
2008). Criteria for these lessons are tasks that involve problem solving and reasoning strategies,
communication with classmates and a connection to other math concepts, principles and thinking.
According to NCTM (National Council of Teachers of Mathematics, 2000) as well as Coffey and
Richardson (2005) it is extremely helpful for students to make predictions before conducting any
experimentation or task and then comparing these predictions with the actual outcomes, as this will
correct probability expectations. Edwards and Hensien (2000) believe that the discussion at the end
of every probability lesson is very important for students as it clarifies and refines their thinking.
When teaching probability, physical resources are particularly useful as they allow children to
become actively involved in their learning. Resources such as dice, coins, cubes and spinners are all
extremely helpful tools in teaching probability and give children a variety of different experiences
when it comes to planning lessons. Tally’s, charts and diagrams are also necessary when it comes to
the teaching of probability as it allows students to record their data and visually analyse and
rationalise it (Edwards and Hensien, 2000). Van de Walle, Karp and Bay Williams (2003) believe
that exploration through activities with such resources and tools are far more beneficial to students
compared to formal definitions. Students need to come to terms with probability through there own
experiences carefully aided by the lessons wisely selected by the teacher.
Critique of the Curriculum (319 words)
According to AusVELS the ideal time to introduce student’s to chance and probability is Year
Level One, which is also supported by Watson and Kelly (2002) who conduct research using six
year olds related to their level of thinking when it comes to probability. The research demonstrated
that although the children were ambitious with their ideas and responses they were not quite at the
level to complete more advanced probability work. However, in saying this AusVELS only shows
three phrases to be used by Level one students; “Will happen”, “Won’t happen” and “Might
happen”, where as Van de Walle Karp and Bay-Williams believe that starting with “Impossible, or
“Possible” is the way to begin probability education which is listed as a Level Two guideline. In
order for Level three students to be able “identify and describe possible outcomes” they will have
to have a clear knowledge of the sample space (Jones, 2005). Level Five states that students are to
“list outcomes of chance experiments involving equally likely outcomes”, however in Edwards and
Hensien’s study (2000) the children although Year five had no previous experience with probability
but were firstly being introduced to equal chance. This demonstrates that the notion of equal chance
can be explored well before the Year Level five, and maybe even as early as Year Level one.
Although AusVELS has designed a year by year guide to teaching probability a lot is relient on the
group of students that are in the classroom. Some classes may exceed the probabilistic thinking of
the level required for them and therefore the teacher can introduce concepts considered by
AusVELS to be of a higher level. According to Jones (2005) it is not in any way rational to think
that a student’s probabilistic thinking will grow in a uniform manner, ordered through the levels of
the guidelines, and of course some diversity will generally be expected as for all curriculum.
Conclusion (110 words)
Probability is a concept that many students and teachers a like struggle to fully comprehend. In
order for teachers to effectively educate their students, they themselves need a thorough knowledge
on the topic. Teachers also need to be able to recognise misconceptions their students are having
and are able to implement strategies that address and clarify the problem. Teachers must use
resources to educate the children, allowing the children to experiment themselves with the notion of
chance rather than giving them the answers.
Probability is an important part of the primary school curriculum that lays the fundaments for data
and statistical analysis that will be explored in their secondary education.
Total Word Count: 1629
References
Coffey, D. C., & Richardson, M. G. (2005). Rethinking Fair Games. Mathematics Teaching in the
Middle School, 10(6), 298- 303. Retrieved from http://www.jstor.org/stable/41182088
Barnes, M. (1998). The Australian mathematics teacher. Dealing with Misconceptions about
Probability, 20(1), 60-63. Retrieved from
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Fischbein, E. (1975). The Intuitive Sources of Probabilistic Thinking in Children. Boston, MA:
Reidel Publishing Company.
Edwards, T. G., & Hensien, S. M. (2000). Using Probability Experiments to Foster Discourse.
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Jones, G. A. (2005). Exploring probability in school: Challenges for teaching and learning. New
York: Springer.
McMillen, S. (2008). Predictions and Probability. Teaching Children Mathematics, 14(8), 454-463.
Retrieved from http://www.jstor.org/stable/41199187
National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for
School Mathematics. Reston, VA.
Nicolson, C. P. (2005). Is Chance Fair ? One Student's Thoughts on Probability.Teaching Children
Mathematics, 12(2), 83-89. Retrieved from http://www.jstor.org/stable/41198663
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and Middle School
Mathematics (8th ed.). Upper Saddle River, NJ: Pearson.
Watson, J., & Kelly, B. (2002). Emerging Concepts in Chance and Data. Australian journal of early
childhood, 24(4), 24-28. Retrieved from
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