Math and Test Preparation Overview

Without minimizing the importance of the rest of the curriculum, math is the central component required to effectively prepare adult women to succeed in the construction industry.  Not only is mastery of basic math skills essential to passing the aptitude tests administered by many apprenticeship programs as a means of selecting and/or ranking applicants, but, since trades work typically requires strong math skills, entering an apprenticeship program with these foundational skills can mean the difference between success and failure.

The program described here is short-term, devoting an average of 36 hours to math and test preparation instruction, meaning that it is primarily effective as a refresher course for women who have been exposed to these concepts in the past even if they have forgotten much of what they learned. Keep in mind that this curriculum evolved within a specific context, so you may require a more or less intensive course depending on the prevalence and content of apprenticeship program entrance exams in your area as well as the needs of your students and those of the apprenticeship programs you are targeting.

tradeswoman measuringThere are a few important notes to make about the philosophy and challenges of this course. Typically institutions test and assign students to the math class most appropriate to their level of skill. TOP, however, is intended to serve all women interested in trade careers.  Though there is a minimum requirement for entry, you can expect a wide variety of skill levels in the class. To ensure that all students have an opportunity to learn, we generally begin each new topic area with a pre-test and then divide students into small work groups based on the results. This allows the teacher and tutor to focus on those who are struggling to master required concepts while challenging more skilled students with advanced materials. Through cooperative learning groups, math can be presented and worked on in an amicable and relaxed setting, removing a fair amount of the anxiety and stress many women associate with the subject. These groups also foster immediate rewards and confidence building among the women as they work out problems together.

To make the most of the short period of time dedicated to math and identify any individual difficulties in learning the material, the program gives daily quizzes and homework assignments. Quizzes are graded and returned before the next quiz or presentation to give students immediate feedback on their progress.  Frequent quizzes also provide instructors with the opportunity to address any individual learning issues before the student falls too far behind the class. Because of the fast pace, instructors will not be able to repeat concepts until everyone in the class is proficient. Instead, CWIT has found that individual and group tutoring outside of class hours to be an effective tool in meeting the specific learning needs of program participants. Tutors are available before each class and for scheduled appointments.  For the most part tutoring is voluntary, though students who are not achieving adequate progress may be required to attend tutoring as a condition for continuing in the program.

measuring instructionMeasuring is taught in conjunction with math, beginning on the first day of class until students understand the concept and can measure to the 16th of an inch.   Once they have mastered measuring, the program introduces students to basic blue print reading skills.  Though not necessary in terms of test preparation, being able to read a blue print is at the very least a useful skill and may well be a required one.  This course will familiarize students with:

  • The meaning of working drawings and their use
  • Measuring tools and the concept of drawing to scale
  • Lines and symbols used in plans
  • Types of plans (elevation, floor plan and section)
  • Role of architect, general contractor and developer
  • Mechanical drawings, plumbing, electrical and heating system symbols.

For the first seven weeks of instruction, the program uses the following text books:

  • S. Gypsum Advisory Service, “How to Read Architectural Drawings”
  • C. Thomas Olivo and Thomas T. Olivo, “Basic Blue Print Reading and Sketching”, “Section 1: The Alphabet of Lines”

Blue print skills reading skills are reinforced through practical application during hands on training.

measuring exerciseIn addition to math, most apprenticeship program entrance exams in the Chicago area commonly include reading, numerical reasoning, spatial visualization, and mechanical reasoning.  Mechanical reasoning refers to an applicant’s ability to understand some basic laws of physics, including force and motion, weight and mass, and simple machines such as levers, inclined planes, pulleys, screws, wheels and axles, and wedges. As intimidating as this might sound to some participants, most of these questions are based on common knowledge.  The program makes use of a number of resources, including the Bennett forms.   Spatial visualization, or the ability to visualize in two or three dimensions, is, in the Chicago area at least, tested through paper folding or hole punching exercises such as those found on the program’s pre-test.  Beginning with a square of paper, the class builds their skills by walking through the steps of folding, punching holes, and unfolding the paper to confirm their answers.  In addition, there are numerous activities available to build spatial visualization skills, some of which are included in the hand-outs section. For consistent practice, one problem each of mechanical reasoning, spatial visualization and numerical reasoning are presented every day. These problems are included in the hand-outs as “daily challenges” or instructors can select the problems most appropriate to their class level and write them on the board.

Because it is difficult to achieve reading gains within the scope of a short term training program, the reading level required for entry into the program is higher than that for math (approximately 8th grade on the reading pre-test). At the same time, the program encourages students to read and is currently providing much of its workforce readiness curriculum through a book club led by Literature for All of Us.  The curriculum is included is included under Workplace Readiness.