Generalizations and symbolization in algebraic thinking
After reading chapter 1-4 from Kiss my Math (McKellar, 2009) and Chapter 14 from
Elementary and Middle School Mathematics: Teaching Developmentally (Van de Walle et al., 2013),
discuss the following (I have attached all of the chapters):
In Chapter 14 of Elementary and Middle School Mathematics: Teaching Developmentally (Walle et
al., 2013) Kaput argues that generalizations and symbolization are essential aspects to algebraic
thinking.
o What do each of terms, �generalizations� and �symbolization,� mean?
o What examples of generalization and symbolization might be found in your curriculum?
o What strategies do you use, or could use, to develop an understanding of symbols? Utilize the
McKellar (2009) text for ideas.
GENERALIZATIONS AND SYMBOLIZATION IN ALGEBRAIC THINKING 2
Word count: 340
Generalization in the mathematical context refers to building up on the learners’
previous knowledge by showing them the relationship between the new concept and what
they know about the topic. On the other hand, symbolization is the use of signs to represent
real life occurrence when solving problems that are pertinent to the decision-making process
(Van de Walle et al., 2013).
The application of generalization takes place in arithmetic when it comes to
operations, exploring patterns, and in the hundreds chart. In operations like algebra,
generalization is used when it comes to coming up with solutions without necessary having to
list the numbers. Secondly, it is used in exploring patterns, and generalization does show the
relationship that is present between various concepts. In the topic of integral, when students
understand that the concepts are linked to differentiation. They can use the previous
knowledge to derive solutions on the new concepts. Lastly, in the hundreds chart
generalization is used in explaining the concept of enumeration to students. They master that
after every ten they proceed to the next level this forms the foundation of mathematics (Van
de Walle et al., 2013).
Contrariwise, symbolization is applied in the equal sign and variables. The equal sign
is widely used in showing the relationship that is present in the number system. The equal
sign does used to represent balance where quantities on different sides are equal. Moreover,
GENERALIZATIONS AND SYMBOLIZATION IN ALGEBRAIC THINKING 3
symbolizes are used in variables to show unknown values in calculations and are always
represented by letters. Variables are also used to simplify complex expressions and equations
for ease in calculation by students (Van de Walle et al., 2013).
The use of symbols that students can easily relate to like describing the various
variables regarding pearls and bag of pearls. The teacher can also use visuals to enhance the
comprehension of the lesson. Finally, allowing the students to formulate their examples of
mathematical concepts under different constraints based on their understanding. Active
participation makes it easy for students to understand symbols (Mckellar, 2009).
GENERALIZATIONS AND SYMBOLIZATION IN ALGEBRAIC THINKING 4
References
McKellar. D. (2009). Kiss my math: showing pre-algebra who’s boss. Penguin.
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.
