Evaluating Number Sense in Workforce Students
The new high school equivalency tests ask adults to perform at a level of critical thinking that they may not have been introduced to in their earlier education. This kind of thinking means that a person is able to look at the details and see the big picture or look at the big picture and pick out the relevant details for a given situation. This kind of thinking requires keeping track of the WHOLE (the main idea) and the PARTS (the details) at the same time, while considering the relationships between them. While part-whole critical thinking is important in all academic areas and in problem-solving on the job, it is especially central to math success.
Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of part-whole thinking. This concept, needed to understand fraction and percent relationships, carries over as a grasp of the relationship between details and the main idea in factual prose, in critical thinking in job situations, and on the current high school equivalency tests.
Assessing learners for their understanding of the part-whole concept allows teachers to help students strengthen either their understanding of the part-whole concept or their applied skills.
Adult educators will find this article interesting and, perhaps, be surprised that so many adults are not already sensitive to the requirements of a simple number line (equal spaces between all consecutive numbers). This concept is particularly important in work settings that assume workers’ ability to use measuring devices accurately. The resource clearly describes a task that can be immediately used with learners for formative assessment and also provides samples of student work that can be studied and analyzed by teacher study groups and/or groups of learners in a classroom setting.
It will be useful to new and experienced adult educators both for its description of problems in adult students understanding of part/whole concepts as well as for giving instructors a very useful tool for quick, easy, and inexpensive assessment of those concepts. The author also suggests reasons for why students lack these concepts including brains that were not physically ready for processing this information due to young age, toxic stress in childhood (e.g., poverty, emotional and physical abuse) and developmental disabilities or traumatic brain injuries. While the information is nothing new to experienced adult education instructors, the author provides a way to see specific results of childhood stress in a way that will ring true to community college instructors in workplace development programs as well as adult basic education classes. The author asks the reader to check his or her assumptions about learning, to modify their teaching, and always to be aware of the building blocks leading to mathematical understanding.