A presentation on "Building Taxonomies" and "Composing with Keywords" as language strategies in teaching mathematics

1. Language
Strategies
I. Building
Taxonomies
II. Composing
with
Keywords
Presented by:
JOEY F. VALDRIZ
Teacher III
DIVISION
TRAINING OF
TEACHERS ON
LANGUAGE
STRATEGIES IN
TEACHING
MATHEMATICS
Date: October 22-23, 2018
Venue: San Fernando North
Central School, Tanqui, City of
San Fernando, La Union

2. (Countryman, 1992)

3.  Mathematics has a specialized vocabulary.
 It relies upon definitions of key terms.
 Vocabulary is as critical to understanding
mathematics as numbers and symbols.
 Mathematical language builds on the existing
structure and logic of common language
(NCTM, 2000)

4.  The use of the language may differ between
the common language we use in our everyday
activities and the language we use in
mathematics

7. knowing and understanding
estimating, computing and solving
visualizing and modeling
representing and communicating
conjecturing, reasoning, proving
and decision-making
applying and connecting

8.  organize and consolidate their mathematical
thinking through communication;
 share their mathematical thinking coherently
and clearly to peers,teachers, and others;

9.  analyze and evaluate the mathematical
thinking and strategies of others;
 use the language of mathematics to express
mathematical ideas precisely.

10. • gain insight into their students’ thinking
• diagnose their students’ misconceptions
• assess students’ thinking habits and attitudes
• evaluate their own teaching techniques

11.  A taxonomy is a classification system that
organizes information on a specific topic or
concept.
 Taxonomy is a system for “having words”.

12.  In this workshop, it refers to a collection of
words related to a specific mathematics
topic.
 The purpose of this strategy is to let
students accumulate and keep track of
their mathematical vocabulary.

13. ◦ Assess both prior and new knowledge of topics.
◦ Monitor progress in mathematical jargon.
◦ Serve as basis for writing activities in the discipline.
◦ Build awareness for vocabulary.
◦ Develop cooperative learning experiences for
students.

14.  Assess the extent of personal and
collective vocabulary in selected
mathematics areas.
 Appreciate the specialized vocabulary of
mathematics.
 Recognize the importance of words in the
teaching-learning process.

15. 1. Group yourselves into smaller groups of 5
members.
2. Each group will select a theme or an area from the
following: Algebra, Numbers and Number Sense,
Business Mathematics, Calculus, Geometry,
Measurement, Trigonometry, Statistics and Probability,
and Symbols and Notation.
3. Individually, write down a word or words for each
letter of the alphabet that is related to the subject
theme assigned to the group.
4. Build the group taxonomy using the template
provided:

16. SubjectTheme: GEOMETRY
Letter Words
A angle, axis
B bisect
C circle, cylinder, cube
D diameter, degree
…
W width
X
Y
Z

17. 3. Post your taxonomy in the “gallery” toallow other
groups to appreciate and evaluate.
4.Assign a member to present your group’s work. Focus
on the following:
a. Explain why some words are known by all
members while other words are known only by
some members.
b.Identify some words in your taxonomy which you
find difficult. Explain why you consider these
difficult.
c.Did your group experience difficulties in making
your taxonomy?Why or whynot?

18. Directions:
1. Retrieve your original taxonomy from the
“gallery”.
2. Exchange your group’s taxonomy with
another group.
3. Review the taxonomy you received.
a. Fill in the gaps where no word was provided.
b.Add more words to the list, if possible.
c. Encircle words that do not fit the theme.

19. 3. Post the revised list in the“gallery”.
4. Present the revised list focusing on the
following:
◦ Which terms can be considered fundamental or
basic to the subject theme? Why do you say so?
◦ Which terms can be considered as specialized
(jargon), if any?Why do yousay so?
◦ Did you remove any word/s from the list or at
least consider removing word/s from the list?
Explain.
◦ Did you encounter any difficulties in revising the
taxonomy?Why or why not?

20.  As teachers, which is more important: an
extensive cross-discipline vocabulary or an
intensive in-discipline vocabulary?
 How important is vocabulary to the learning
process?
 Does having a large vocabulary automatically translate
to better understanding of mathematics?

21.  Teachers can use “BuildingTaxonomies” in:
◦ Pre-assessment, to determine the extent of
student knowledge of subject matter
◦ Student journals, where students can track the
progress of their vocabulary in the subject over a
school term
◦ Sharing exercises, where students can
exchange words and share what they know about
the words
◦ Building “word banks” for use in other
activities

22. Objectives:
1. Use words from the taxonomy to compose
sentences and paragraphs.
2. Construct clear and coherent sentences and
paragraphs by using words and grammatical rules
correctly.
3. Assess each others’ constructed sentences and
paragraphs and suggest changes when
necessary.

23. Countryman (1992)

24.  allows students to develop their fluency in
composing so that they could better
understand the concepts you are teaching
 helps students reflect on the meanings of
mathematical words/terms, clarify their
understandings through the process of association,
and incorporate the words into a statement that
shows how each word relates to other
mathematical words

25. Directions:
1. Each member of the group will select three words
from your original taxonomy.
2. Use all the three words to compose one
mathematically correct sentence. You may change
the form of the word, if necessary.
3. Write the group result in a Manila paper using
the prescribed format. Shade the words from
the taxonomy.
4. Post your work for other groups to
appreciate and evaluate.

26. Theme/Area Keywords Sentence (Concept)
Geometry area
triangle
rectangle
The area of a triangle is equal to half the
area of a rectangle.
Statistics graph
axes
gather
I represented the data that I gathered for
my assignment through a graph using a
Cartesian Plane with x- and y-axes.
Trigonometry sine
hypotenuse
right triangle
SineA in right triangle ABC is the ratio
of opposite side BC and hypotenuse
AC.

27. Theme/Area Keywords Sentence (Concept)
Calculus range
cosine
sine
The range of cosine and sine functions is in the
interval [-1,1].
Business Math Deduction
Cost
Discount
There is a deduction of Php 14.00 on the
cost of that good with label “5%discount”.
Geometry Opposite
sides
Rectangle
Parallel
Opposite sides of a rectangle are parallel.

28. Theme/Area Keywords Sentence (Concept)
Algebra degree
constant
zero
The degree of a constant function is zero.
Symbols and
notations
ratio
zero
undefined
The ratio of any integer and zero is undefined.
Statistics mean
summation
data
He was able to compute the mean by dividing
the summation of all the scores to the
number of cases in the given data.

29. Theme/Area keywords Sentence (Concept)
Analytic
Geometry
point
ray
line segment
The point, ray and line segment are
the elements of a line.
Measurement tape measure
meter stick
ruler
The tape measure, as well as the meter stick
and ruler, is used to measure units of length
such as,yards,feet,inches,meters,centimeters,
and millimeters, but not units of distancessuch
as kilometers and light years.
Trigonometry angle
elevation
line of sight
The angle of elevation is formed from the
horizontal line of sight and the object above the
observer.

30. 1. Were the words used correctly in the
presented sentences?
2. Based on your own classroom experience,
what learning issues will probably arise if
you give the same exercise? How would
you deal with it?
3. What probable value would this exercise
have to the learning process?

31. Teachers can use “Composing with Keywords” in:
Assessment, to know if students see and
understand the relationships between words
Reflection Exercises, for students to realize what they
know and what they still need to know
Remediation, to identify terms or relationships among
terms that are difficult to students and to provide an
opportunity for clarification or redirection

32. 1. Using your taxonomy,construct a paragraph
using as many words in the taxonomy as
possible. Double underline the words in
your paragraph that come from the
taxonomy.
2. Using the words in the taxonomy, write 3
sentences to be converted into symbols. Pick
any one of these representations and write a
new sentence based on it.

34. Presentation of Dr. Estrella R. Pacis during the Regional Training
of In-service Teachers on Language Strategies in Teaching
Science and Mathematics on August 1-3, 2018 at the Grand
Octagon Resort, Laoag City