High school students are forced to balance many different responsibilities when pursuing their education while preparing for the next phase of life, such as preparing to enter the workforce or apply to college. Demanding subjects like geometry can have a strong impact on the kinds of options open to students after high school. Students’ ability to succeed in courses like geometry is often key to their ability to be accepted to a college or to find stable and high-paying work, especially in STEM fields.
Geometry does not have to dampen students’ hopes and dreams, though, because, with a few essential tips, high school students can master some of the most difficult topics in geometry.
Enlisting Expert Help
One of the first and most important tips a high school student needs to conquer the dreaded geometry class is to not be afraid to enlist the help of an expert. The guidance of an expert tutor is a highly valuable resource because most high school students simply do not enter their geometry classes with the skills they need to succeed in the class. Most mathematics courses in primary school and the middle grades focus on numeracy and arithmetical and algebraic processes, leaving students unprepared to engage in the kind of spatial reasoning required to succeed in high school geometry (Lowrie et al.; Szabό et al.).
With the help of an expert tutor, however, students learn to translate their numeracy, arithmetical, and algebraic skills into geometric concepts, forms, and processes.
Using Augmented Reality
One of the most significant challenges that high school geometry students face is in the ability to visualize, manipulate, and analyze shapes and the relationships between them. For example, high school students often have particular difficulty with the geometric concept of congruence, which refers to the exact equivalency between shapes in regard to angles and sides.
Testing for congruence often involves the use of rigid forms which allow shapes to be overlaid in order to better ascertain their geometric sameness.
Augmented reality, though, is often a better option than rigid forms because it allows students to easily manipulate geometric forms, manipulating three-dimensional shapes to analyze the shapes and relationships between them (Gargrish et al.).
Using Video Modeling in Geometry Word Problems
Another important challenge high school geometry students face is in dealing with geometry word problems. These are often difficult to translate into the kind of geometric visualizations required to address the problem effectively. Video modeling enables students to create digital images of the geometric forms being described in the word problem.
Of the benefits of video modeling, Satsangi et al. write, “Within the problem-solving process, problem representation is considered the first step wherein students interpret a problem and its given information into an understandable format and then transfer necessary information into a mathematical, visual, or mental model for solving the problem” (pp. 309-310).
In other words, if geometry students can see it, they can begin to solve it!
Using Problem and Task-Based Learning
Alongside challenges with spatial reasoning, high school geometry students also often struggle to understand how geometric concepts and processes relate to the real world. However, experienced and successful high school geometry teachers know the best method for learning geometry is to understand how it works in “real life.”
For that reason, high school students should use active learning principles to apply the concepts they’re studying to familiar tasks, scenarios, and situations.
Cherif et al., for instance, have created a series of active learning tasks that enable high school geometry students to learn how to define and analyze plane and polygonal shapes, to assess volume, and to translate three-dimensional shapes into two-dimensional pictorial representations.
Task-Based Learning to Help Students Work with Proofs
Proofs are an essential element of geometry, but high school students often find working with proofs to be a particular challenge.
Komatsu et al., though, developed a task-based questionnaire that helped high school students not only learn to work with proofs but also to understand, analyze, and apply them more effectively. Through a systematic, step-by-step task-based approach, students are able to learn by doing.
Suddenly, proofs are no longer abstract words and formulas to be memorized, but tangible tools and practical processes with real-world applications.
Students who struggle with geometry are by no means alone, and it is not difficult to understand why. High school students are rarely equipped with the spatial reasoning skills they need to succeed in their courses due to the focus on numeracy, arithmetic, and algebraic reasoning in earlier grades.
However, there are many strategies that high school students can use to conquer the geometry beast. This includes enlisting the help of expert tutors, using video modeling and augmented reality, and focusing on task-based learning and real-world applications of geometry.