Content Standard
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Assignment 2.1a
Name Removed
National University
MAT 674
Content Standard
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Abstract
Employing a close examination of content standards proposes that they consist of
multiple elements of learning for students. These elements consist of specific facts, principles,
attitudes, and skills that teachers seek to transfer through various means of instructional practice.
This includes presenting students numerous opportunities to demonstrate their levels of
understanding and fluency in content material. By providing product assignments that align with
different aspects of Garner’s multiple intelligences, students can practice what they have learned
in ways that speak to their specific predispositions to learning. The following are two charts
created to illustrate these two aspects of content standard integration within the classroom.
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Levels of Learning: Mathematics Content Standards:
The following table was created with 8th grade mathematics content standards in mind.
Specifically, content standards:
Expressions and Equations (8.EE)
5. Graph proportional relationships
6. Derive equation y=mx+b for lines
7.a. Give examples of linear equations
Within these content standards there exist different levels of learning in which students are
required to assimilate as they progress through the curriculum and develop the skills and
knowledge necessary to successfully achieve mastery of each specific standard. In essence,
content standards can be viewed as a foundational framework of learning that is required within
each grade level, but also as a means to further delineate instruction into aspects that address
different facts of comprehension for students within the classroom.
Level of
Description of Content Standard
Learning
Fact
Understand proportional relationships that include linear tendencies between
variables.
Concepts
Synthesize data to concisely identify elements of linearity through both algebraic
and graphical means of construction.
Principles Extrapolate characteristic equations for linear data, utilizing these found functions to
visually represent tendencies and relationships between variables.
Attitude
Students: “I know what to look for when trying to prove that a function is a line as
well as data that fits into the realm of linearity.”
Skill
Given a set of data, students will be able to find a linear function that describes the
relationship between two variables, using their knowledge of both graphical
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extrapolation and algebraic manipulations of the standard equation for a line.
Product Assignments: Garner’s Eight Intelligences:
The following is a chart created to illustrate the application of Garner’s Eight Intelligences (i.e.
Verbal/Linguistic, Logical/Mathematical, Spatial, Body/Kinesthetic, Musical, Interpersonal,
Intrapersonal, Naturalist) to specific assignments that can be utilized within the classroom to
assess levels of understanding to the mathematics content standards that were suggested in the
previous section. By having multiple avenues of assessment for students that each require
elements of the different predispositions to learning, instruction becomes most effective in
addressing the needs of all students within the classroom while requiring students to experience
content in different settings and modalities.
Garner’s
Example of Assignment and Rationale
Intelligence Area
Verbal/Linguistic
Students will be tasked individually to take a specific example of a
linear equation, describe its important characteristics (i.e.
slope/intercepts), graphically represent it within a coordinate plane, and
describe their findings with a partner or in whole-class settings. This
assignment provides students the opportunity to practice the
foundational skills necessary in proving linearity. By having them
present their findings orally, students are being exposed to an
assignment that requires them to utilize academic communication which
inherently addresses the specific intelligences within the
verbal/linguistic realm.
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Logical/Mathematical Considering the logical/mathematical setting of the content initially,
appropriate assignments for this area of intelligence would include using
data to extrapolate linear equations, being provided characteristics of a
line (i.e. slope, intercepts) to find its standard equation, and visa versa.
These exercises require students to utilize the logical nature of the
mathematical techniques they acquire throughout the unit. By providing
opportunities for students to work forwards and backwards in
extrapolation, a more concerted effort in deeper synthesis of strategies
must be attained to successfully complete the assignment.
Spatial
For spatial intelligences, an emphasis is placed on elements of
visualization within the content standard. In the subject of linearity,
graphical representations are an important aspect of understanding what
equations actually represent and how numerical relationships change
over time. Hence, by providing students an assignment in which they
take a set of data or characteristic equation and graph it within a
coordinate plane requires them to illustrate elements of linearity while
also providing them a means to experience the spatial aspect of content
material.
Body/Kinesthetic
In mathematics, the use of strategies that align with body/kinesthetic
tendencies are often utilized (i.e. counting on fingers). For linearity, this
aspect of intelligence can be directly applied to identifying lines as
increasing, decreasing, or neither. An assignment can be proposed in
which students are required to find a way to show with their arms the
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central tendency of a graphed line. (i.e. diagonal created when right arm
is up and left is down represents an increasing function) In this, students
continue to deepen their understanding of linear functions by developing
vocabulary that concisely describes elements of linearity. Moreover, by
establishing a system that pairs with their body, students will be
provided a useful tool in future identification of central tendencies in
graphs.
Musical/Rhythmic
An assignment that can be applied to address musical intelligences
would be to task students with constructing a song or poem that includes
academic vocabulary pertaining to linearity as well as their definitions. It
is clear that having a strong grasp on academic concept vocabulary is an
essential element of successful learning experiences within the
classroom. Hence, by allowing students the opportunity to creatively
demonstrate their understanding while also practicing specific concepts
provide an effective way to incorporate variety and usefulness within a
product assignment.
Interpersonal
Interpersonal intelligence asserts the importance of interaction among
students during the learning process. This is most often addressed during
assignments that are given in the small group or paired setting within a
lesson. An assignment such as, creating an individual linear function and
its graph then exchanging their graphical representation or linear
function with a partner. Then each student will graph or extrapolate the
function and ultimately compare their findings for accuracy and
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correctness. This activity allows students to discuss elements of linearity
with each other while also individually practicing the skills and
techniques required in the assignment. Students practice their
communication skills as well as their cohesiveness as a valued
participant in the classroom community.
Intrapersonal
Intrapersonal intelligence is characterized by the understanding of one’s
own level of understanding within the content area. An assignment such
as a, “ticket out the door” prompt in which students are tasked with
describing what they have learned during the lesson and what they still
have difficulties with provide them with a chance to examine their
relative levels of understanding and synthesis in specific concepts within
the material. This allows students to consider the steps to take in order to
increase their understanding while also informing the instructor of the
areas of improvement and re-teaching that need to be assessed in
subsequent lessons.
Naturalist
Naturalist intelligence requires connections between content and their
applications in the real world. For mathematics, real-life applications are
abundant and diverse in both setting and utilization. A research
assignment can be provided to students in which they must find an
application of linear functions in the real world (i.e. distance formulas,
temperature conversions). This allows students to be exposed to the
importance of what they are learning and the relative value that it has in
its application to different settings, which ultimately increases
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engagement and motivation in continuing to develop their understanding
of mathematical concepts.
Content Standard
References:
California Department of Education Department of Education , (2010). Common core state
standards for mathematics. Retrieved from State Board of Education website:
http://www.cde.ca.gov/be/st/ss/
Ventriglia, L. D. (2010). Best practices: Differentiated instruction, the rule of foot. (8th ed.).
Mexico : Younglight Educate. DOI: www.younglighteducate.com
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