Higher Level Thinking Questions and van Hiele Levels

1.  What level(s) of Bloom’s Taxonomy most closely align with the level(s) of the van Hiele Model? Justify your thinking.

Level 0:  Concrete is most similar to Bloom’s knowledge.  The student can identify and compare geometric shapes.  Comparing shapes at this level is not necessarily at Bloom’s understanding level.  I think it is more of a visual comparison.

Level 1:  Analysis is similar to Bloom’s understanding level.  This is where the student could examine the shape and classify it by its properties.  Analysis could also be compared to Bloom’s apply level.  It’s at this point that students can apply formulas and compute areas.  They could also look at different shapes and compare their perimeters and area.

Level 2:  Informal deduction corresponds to Bloom’s analysis level.  Students begin to analyze and differentiate properties of shapes and apply them to one another.

Level 3:  Deduction must be at Bloom’s synthesis level.  Using deduction requires a thorough understanding of geometric principles and combining them in such a way to formulate theorems.

Level 4:  Rigor is at the highest level of thinking so I would compare it to Bloom’s evaluation level which is also is the top of the scale. 

2.   Answer the question asked in the article: “How can you use the van Hiele levels to help students learn mathematics?”

I think van Hiele’s levels relate closely to Vygotsky’s zone of proximal learning.  Students can not learn something unless they are ready for that stage of learning.  van Hiele’s levels demonstrate this as well.  We can not ask students to perform at a level higher than they are currently on.  As teachers, we must evaluate our students and where they fall within this framework.  Activities must be presented to them at their levels.  As the previous article showed, one lesson may cover more than one level.  Students will simply think at different levels and be able to apply concepts in a variety of ways. 

3.  Review the “Guiding Questions for Group Discussion.” Using the Questioning Cue Words from Module 4 < link to table from previous module>, develop additional questions that you could ask students if you were to use this lesson in your classroom. Use the Bloom’s Question worksheet you used in Module 4.

Use the tiles to configure two different shapes with the same perimeter.  Do you think that their areas will be equivalent as well?  Test your prediction.  Compare the two areas? 

Construct a 3, 4, and 5 triangle.  Using each of the sides construct squares.  Evaluate a² + b² = c².  Now using the same 3, 4, and 5 triangle construct triangles from each of the sides.  Predict whether the same holds true?  Does a(triangle) + b(triangle) = c(triangle).  Discuss why or why not?