§111.35. Precalculus, Grade 11
(b) Introduction.
(1) In Precalculus, students
continue to build on the K-8, Algebra I, Algebra II, and Geometry foundations
as they expand their understanding through other mathematical experiences.
Students use symbolic reasoning and analytical methods to represent
mathematical situations, to express generalizations, and to study mathematical
concepts and the relationships among them. Students use functions, equations,
and limits as useful tools for expressing generalizations and as means for
analyzing and understanding a broad variety of mathematical relationships.
Students also use functions as well as symbolic reasoning to represent and
connect ideas in geometry, probability, statistics, trigonometry, and calculus
and to model physical situations. Students use a variety of representations
(concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and
technology (including, but not limited to, calculators with graphing
capabilities, data collection devices, and computers) to model functions and
equations and solve real-life problems.
(2) As students do mathematics, they
continually use problem-solving, language and communication, connections within
and outside mathematics, and reasoning (justification and proof). Students also
use multiple representations, technology, applications and modeling, and
numerical fluency in problem-solving contexts.
With teaching what would be junior level
students in High School, it would be best to keep in mind that they need to
develop assessment skills for this course. From the TEKS, I understand that the
students need to be able to look at graphs, functions, and diagrams to
understand what the question is asking. They need to be able to explain what is
going on in the problem. Overall they will need to be taught skills that allow
them to analyze the problem and solve thru definition, decryption, calculating
domain and range, finding symmetry, and looking for behaviors, continuity,
asymptotes, etc. Students would also be required to memorize formulas or
recognize which are to be used in a certain cases. Another requirement would be
to calculate different equations without the usage of a calculator, going back to the age of basic math.
In Precalculus, there really isn’t a single
concept that is more important than any other. Each concept has be already
taught or is being taught for the sake of expanding the knowledge. They will
come to understand an variety of representations, tools, and technology to
model functions and to solve equations. As the students are exposed to the
numerous examples, they will develop small tricks of the trade to solve their
problem and develop into problem solvers. They then create a language and
forming communication skills to make connections and deduce reasoning. Students
can also develop a sense of independence as they learn traits to solve problems
without the use of calculators and to simple apply simple math to their work
and finding the answer where it is.
There are many helpful tips to help students understand TEKS concepts. TEKS can be very difficult for some students because it is an overall knowledge of different concepts in different subjects. Students may have a hard time understanding all of these concepts and it can be too much for students to remember. Math deals with numbers and people struggle with numbers, this is why accountants and other people in the math field receive the pay they do because only a few people really understand math.
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