Yes. ProofBlocks are a very natural way for students to visualize geometric proof. Much like paragraph proof, the ProofBlock format is not well suited to proofs that are very algebraic in nature. (If you’re wanting to add to both sides of an equation, it is far more convenient to be showing your steps vertically.)
In most books, proofs requiring the more algebraic steps are found in the chapters on parallel lines and angle pairs. The chapters on proving triangles congruent usually require proofs that are less linear and less algebraic in nature. So we teach proof beginning with the congruent triangle unit and use the unit on parallel lines, transversals, and angle pair relationships to motivate the transition to the more traditional two-column format.
The important point here is that ProofBlocks teach kids how to think about proof, introducing the idea in a way that is easy to visualize and that makes sense. Once they really understand the concept of “proof,” the battle is mostly won, and they can learn to use any format.
What do students need to know before I introduce ProofBlocks?
Different teachers choose to organize their curriculum differently, and to a great extent, we can only speak to our experience. We have always placed ProofBlocks in the third unit of the year, following work on basic vocabulary, segment and angle properties, and logic. (Jinna and I have different approaches to the logic unit including everything from exploring engineering logic gates to generating rules for creating a logical argument by debating possible school rules).
However it is introduced, before a ProofBlock is ever handed to students, they have worked with converses, inverses, and biconditional statements. They have also learned to:
- Name congruent figures
- Distinguish between included and non-included angles
- Determine whether triangles are congruent by SSS, SAS, ASA, or AAS
- Apply the definitions of midpoints, perpendicular lines, and bisectors to geometric figures
Will using ProofBlocks require me to reorganize my curriculum?
Probably, but we understand the difficulties of managing district and department pacing plans, and the extent to which you reorder topics is up to you. We prefer teaching the congruent triangle unit before that about parallel lines, even though our textbooks present that material in the opposite order. The proofs in the congruent triangles section of our texts, however, require knowledge of the previous chapter’s angle relationships.
Our solution: We supplement with a couple weeks of worksheets whose congruent triangle proofs do NOT require prior knowledge. (Incidentally, we’ve provided a number of these worksheets to you as part of our online resources.) As they master proofs combining congruence postulates, reflexive property, relevant definitions, and CPCTC (“corresponding parts of congruent triangles are congruent”), we begin the transition into two-column proof. The unit on parallel lines and angle pairs follows and is taught exclusively in two-column format. Finally, we revisit the more complicated congruent triangle proofs in our book that combine all these concepts.
Another solution: Some departments, in an effort to comply with district pacing plans and to avoid reorganizing the textbook so drastically, teach the parallel line unit first, but without the proofs. Then, they start proof in the congruent triangles unit using the ProofBlocks and the supplemental proof worksheets on the Resource pages.
Can I teach two-column proof first, and then use ProofBlocks when we get to congruent triangles?
At the risk of being too blunt… No. There are at least two reasons we discourage this practice:
Concrete manipulatives are not well-received once students have some familiarity with a concept. (If you don’t believe us, take a look at research.) Generally, the students who understand proof in two-columns will want to continue using that format (as they should) thereby making ProofBlocks the lower-status alternative. The students who are confused but not good at judging their level of understanding, will then reject ProofBlocks in both manipulative and drawn format as just another thing to learn, preferring to cling to the familiar two-column format in the vague hope that a miracle will happen and one day it will suddenly and miraculously make sense. Taught in the other order, however, these issues do not arise.
ProofBlocks are designed as an introduction to proof and are efficient in this role. While it is relatively painless to teach and learn proof with this method, and most students find success, the transition to two-column proof is also smooth and purposeful. There are proofs that just ought to be done in that method, and with a firm grounding in “proof,” the benefits of the two-column format are then clear to the students.