Standardized Help Page for Math
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Introduction

     States require districts to test students using standardized measuring tools. In Illinois, the current testing instrument is the ACT. Educators wrestle with the notion of using this test as an instrument, yet it is the device that all districts must use.

     The results from these tests are collected, analyzed and reported. Districts are compared by these tests. The results of the tests may also impact funding to districts, too. Consequently, these tests are very important to communities, educators, students, and teachers.

     In order to afford educational communities with the best chance for success on standardized tests, educators must prepare students in various areas. This portion of MATHguide will help educators plan in order to help students place better on Illinois' testing instrument in regards to mathematics. However, even though other states use different testing devices, the information here can be used for nearly any device, as the ideas fit the general guidelines for most high school learning goals.

     This document is divided into these sections:


     Since the standardized testing devices are in effect, there are some guiding questions one could use to fuel organizations into action. They may serve as a starting point to initiate discussion. The discussion should lead concerned educators to master their crafts to help students score better on standardized tests.
  1. Are you here to teach the content or to teach the student?
  2. How do you respond to tests in which you perform poorly?
  3. If you were a student in a school that was held to standardized tests, how would you perceive educators who did not incorporate learner-orientated lessons to help you perform well on such tests?
  4. What sort of educator would not modify his/her methodologies to help students score better on standardized tests?
  5. Considering the long-lasting impact that a standardized test will have on a community, what will you do to make the results as positive as humanly possible?
  6. Have you recently modified your lesson plans to adjust for standardized testing? Was it successful? How do you know if it was successful or not? Did you share your findings with another educator?
  7. The politics of standardized testing is open for debate and not discussing the issue may be more detrimental than doing nothing at all. However, if you engage solely on the politics of standardized testing without changing what you do, how effective of an educator will you be to the students in your community?

     Please carefully interpret the above questions. They are there to act as a catalyst for all educators and participants within an educational community. This includes teachers, administrators, aids, and parents. These questions are not meant to single out any participants within a community.

MATHguide Materials: Guiding Questions (Word)


     Every district must collectively determine the current level of achievement of its students and what future level of achievement is desired. The testing agency will supply information to districts regarding past test results, which makes the first part of the process relatively simple. The second part of the process is much more involved and requires knowing the community both outside and inside the school(s) in question.

     Nevertheless, leaders in an educational community must set a target. Whether set by a committee or an individual, the target must include a clear and attainable goal. For instance, a certain numerical average may be a target or the number of students who meet or exceed the state standard may be the target. Reaching the target will only result in the case that educators identify certain indicators and work to change teaching practices to affect those indicators.


     ACT has published nine indicators (see the Standards for Transition - Mathematics link below) to help educational communities prepare students for their math test(s).

MATHguide Materials: Indicator Chart (Word)

The table below is a summary of that publication. Click on "Ideas" to access general strategies for approaching each particular indicator.

Indicators
Explanation
Ideas
Basic Operations & Applications
Solve multi-step problems involving concepts such as rates, added tax, percentage off, converting units, and problems that contain averages.
Probability, Statistics, & Data Analysis
Read tables and graphs; translate from one type of graph to another; determine the probability of an event; determine the complement of a probability; read/interpret/manipulate data from tables.
Numbers: Concepts & Properties
Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, the ordering fractions, pattern identification, and absolute value.
Algebraic Expressions
Manipulate basic algebraic expressions, like substitute integers for unknown quantities in expressions, add and subtract simple algebraic expressions, and perform straightforward word-to-symbol translations.
Equations & Inequalities
Solve routine first-degree equations, like problems that involve distances, inequalities, and changes in values between two variables.
Graphical Representations
Comprehend the concept of length on the number line; locate points in the coordinate plane; exhibit knowledge of vertical and horizontal lines and of their point of intersection; exhibit knowledge of slope; determine the slope of a line from points or equations; match linear graphs with their equations; and find the midpoint of a line segment.
Properties of Plane Figures
Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90, 180, and 360); use properties of isosceles triangles; and draw conclusions based on a set of conditions.
Measurement
Compute the area and perimeter of triangles and rectangles in simple problems; use geometric formulas when all necessary information is given; and deal with scale drawings and aspect ratio numbers.
Functions
Describe numerical patterns by referencing various functions such as lines, parabolas, sine waves, absolute value and others; present curves of best fit for particular data sets.


MATHguide Materials: Table of Mathematics Indicators (Word)


     As one can see by examining Table of Mathematics Indicators above, the indicators are fairly broad and the details involve concepts that most effective teachers already use in their classrooms. Teachers can simply introduce mathematical concepts and skills with a higher degree of formality to bring relevance to their own subject matter while also helping students to see the usefulness of mathematics in various disciplines.

     While courses could be totally restructured to accommodate strategies and methodologies that approach these indicators, doing so is not absolutely necessary. Educators can brainstorm activities that incorporate common math concepts and retain the integrity of their courses. When introducing new material, the material can be supplemented with tabular data found in research, graphical data typically found in daily papers, and other common creative avenues.

     Another strategy to implement is the use of comprehensive projects. With the use of models and a thorough rubric, educators can integrate numerous disciplines and maintain course integrity. Reading, writing and computation can be included. Students can be directed to research a number of works, provide a mathematical basis for their findings and conclusions, and then reflect on those findings with the use of summaries.

Indicators
Specific Strategies
Basic Operations & Applications
Consumer Ed: Students calculate tax and costs with tax.
P.E.: Have student convert meters to feet to compare various competition runs with the length of a mile.
Probability, Statistics, & Data Analysis
Health: Have students review charts & statistics related to a certain illness to determine various ratios and probabities.
History: Have students find population statistics from the Census and create graphs.
Numbers: Concepts & Properties
Health: Have students review various products and their nutritional information. Using percentages changed into ratios, students can arrange products from highest sodium source to lowest for comparitive purposes.
Algebraic Expressions
All Subjects: Have students understand the relative value of two quantities. For instance, 'Jorge is ?? years older than Maria,' 'Stalin killed ?? times the number of people as Hitler,' 'The braking distance of the car is ?? feet more than ?? times the speed of a car in miles/hour,' ...
Equations & Inequalities
Keyboarding: Students can calculate their hourly productivity using their keyboarding rates/min through extrapolation, which involves the use of intuitive proportions.
Graphical Representations
Woodworking: Have students calculate the slope of a staircase using existing horizontal and vertical distances.
Properties of Plane Figures
P.E.: Instructor can demonstrate various stances during sports and their relative usefulness as they apply to stability or ability to respond to changes in movement.
Measurement
Functions
All Subjects: To introduce a topic or verify a certain property/practice, bring actual data to the classroom. Show how the data, once graphed, fits a certain type of mathematical curve. Automechanics: The viscosity of oil over time may have an inverse relation. English: I would assume that the more books a person reads the more likely that person is to gain a college degree in a possible quadratic relation.


MATHguide Materials: Table of Strategies (Word)
MATHguide Materials: Math Assessment Helper (Word)


     MATHguide has a section to help students and teachers with the PARCC test. This section will target sample mathematics problems that are likely to be found on the exam.

MATHguide Link: PARCC Problems and Solutions


     Use the links below to help your educational community reach higher standards and research high stakes tests by looking at sample tests. These sample tests will help students achieve on the PSAE, which is Illinois' state examination for juniors called The Prairie State Achievement Examination.

  1. Sample Tests: ACT provides a number of sample exams to prepare for the annual test.
  2. SAT Practice Test Questions & PSAT Practice Test Questions: CollegeBoard provides numerous practice tests that cover math, writing, critical thinking, and more.
  3. Standards for Transition - Mathematics: ACT reports indicators that can be extremely useful for altering/creating methodologies and practices in an educational community.
  4. WorkKeys Foundational Skills Assessments: ACT's comprehensive system for measuring real-world skills.
  5. Holt, Rinehart, and Winston - Test Preparation: Find test preparation for the ISAT and PSAE.
  6. Peterson's ACT Prep: Yahoo! hosts a site that can help students with the ACT.


     Here is more information on state tests from states other than Illinois.

  1. Regents Exam Prep Center: New York's test is called The Regents Exam. Prepare for it with this site.
  2. Ohio Graduation Test: The Ohio Department of Education offers an excellent site for practicing tests, that includes reading, math, science, social studies, and writing.