Why High School Geometry Seems so Difficult?

Why High School Geometry Seems so Difficult?

Geometry in high school often proves complex for the regular high school student. It results from the consideration of its detachment from real life. Further, it also comes from the inability of students to quickly understand the formal proofs. As a result, most teachers have resorted to trying different teaching programs and methods, especially in public schools. However, the success of such teaching methods also comes with contrasting success as at times it may succeed while other times, it flounders

So what makes high school geometry such a complicated subject for students?

Why High School Geometry Seems Complex to Students

  • Absence of early-learning proving and proof
  • Most students encounter geometry at first in high school. Because of this, students might end up thinking that the two-column proof entails the only existing proof. Further, the two-column proof essentially proves impractical in real-time, especially with practicing mathematicians. Students could find it easier if there existed one way of encountering informal proofs at an earlier time than high school, where they can then justify their reasoning and statements.
  • Absence of comprehension when it comes to geometry concepts. Researchers opine that the knowledge of geometry progresses with levels, which can’t get skipped. The levels come as van Hiele, and when students get to high school, they exhibit low van Hiele levels. The levels come from zero to level four, and visually it starts from level one.
  1. Level one entails geometric figures getting recognized from their physical appearance and not their properties. Students with such a level can comfortably recognize shapes regardless of what direction it rests.
  2. Level two entails descriptive or analytic aspects where learners can identify a figure’s properties and recognize the figure by the properties they hold. It cannot become possible to spot differences regarding the necessary properties and additional properties of a particular shape.
  3. Level three entails the relational or abstract, where learners can comprehend and make abstract definitions besides distinguishing between sufficient and necessary conditions of a particular concept and comprehending links between diverse shapes. An example involves triangles. A student can differentiate triangles and conclude that all rectangles qualify as parallelograms. However, not every parallelogram proves a rectangle. Students can informally justify their rationale but still fail to make a formal proof. The stage becomes crucial for a student to reach before getting introduced to high school geometry.
  4. Level four involves formal deduction, where a student can make formal reasoning using axioms, definitions, and theorems. Such a scenario sees a student make deductive proofs beginning from what they know before producing statements that can justify statements supposed to get proven.
  5. Level five entail metamathematical or rigor, where learners can make formal reason and compare diverse axiomatic systems. The level becomes crucial for students who want to pursue geometry in college. The theory proves imperfect at the moment, though it still seemingly models the geometrical thinking progression.
  • A learner’s cognitive development. It deals with the overall cognitive development rather than the geometrical reasoning of students. Cognitive development proves crucial for a student to become capable of comprehending geometry, especially when it comes to the formal operational stage. Such a level will see you become capable of reasoning formally besides knowing and constructing proofs.


Geometry can prove difficult and lead to failure for anyone who refuses to do anything about it. However, you have to consider the above reasons that give geometry a difficult perception that can get easily overcome. 

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