Friday, February 12, 2016

Math problem of the week: 21st century geometry proofs

From Learn NC, which provides K-12 learning materials from the UNC School of Education:

Postulates and proofs: Let's take it to the courtroom!

In this unit, the process of solving proofs is practiced using the comparison and framework of a courtroom setting. Students will work in groups to solve a proof and then defend it in a class courtroom setting.

A lesson plan for grades 9–10 Mathematics

In this unit, the process of solving proofs is practiced using the comparison and framework of a courtroom setting. Students will work in groups to solve a proof and then defend it in “court.” This unit challenges and engages students, while building their confidence as they learn to support their arguments with sound, logical statements and reasons. Students will have both individual and group assessments during these lessons

Learning outcomes

Students will:
  • apply prior knowledge of the definitions, postulates, theorems, lines, angles, and triangles to solve proofs.
  • demonstrate the ability to create a sequential flow of reasoning by writing each logical step in a proof as a separate statement in the left column and writing its justification in the right hand reasoning column.
  • demonstrate a conceptual understanding of how to solve a two-column proof by searching for the answers to higher order thinking questions, revealing a more thorough understanding of the content.
  • be able to make a convincing presentation to a courtroom that a proof is correctly solved.
  • demonstrate proficiency of using inductive and deductive reasoning to solve proofs and problems.

Teacher planning

Time required

Seven to eight class periods (on a block schedule) or fourteen class periods (on a regular class schedule)

Materials needed

  • Geometry proofs — each group is assigned a different proof and each member of the group needs their own copy
  • Group folder documents:
    • Courtroom bellringer activity — one per student
    • Problem-solving circle role cards — one per group
    • Geometry vocabulary chart — one per student
    • Collaborative group work rubric — one per student
  • Trial Guide — one per student
  • “Let’s take it to the courtroom!” rubric set:
    • Teacher observation rubric — one per class
    • Proof rubric for judge — one per group
    • Trial rubric for jurors — one copy per juror for each trial
  • Proofs unit test — one per student
  • Pencils

Technology resources

  • Laptops for research and presentations
  • Presentation software or program (such as Prezi, SlideRocket, SMART Notebook, Word, PowerPoint)
  • Multimedia projector and computer
  • Interactive whiteboard
  • Courtroom 101 video (optional)
  • Teen court video (optional) Note: The video is a teen court case in Florida. The content surrounds a teen that made a bad choice, and it involves the topic of drugs. Please watch the video first to decide if it is appropriate for use in your class.

The Trial Guide continues for another 4 1/2 pages.


Unknown said...

One proof over 14 class periods? Yikes, that sounds like the winner of a competition to see who can waste the most time.

Auntie Ann said...

...and 14 class periods is nearly three weeks....and with a 180-day school calendar, that's 7.8% of the year: on one problem.

Barry Garelick said...

I did it a bit more efficiently as described here.

Anonymous said...

As Perry Mason used to say:

"This is incompetent, irrelevant, and immaterial"

education realist said...

Not much point to doing proofs in geometry anyway. I don't do them anymore, other than in honors classes--and even then, I'd cut it in favor of more algebra.

Auntie Ann said...

I think proofs have a value far beyond mathematics. It is the only time we ask students to systematically, logically, and efficiently think through something, from a starting point to an end goal, with justification given for every action.

It teaches a habit of mind that kids aren't asked to develop anywhere else.

education realist said...

But we don't teach it. We can't. The kids are going on to Algebra 2, and most of them don't know Algebra 1. And for the most part, low ability kids don't get proofs, period. Waste of time.

Momof4 said...

IOW, if everyone cannot do it, no one is allowed; individual ability and interest be dammed! Let no child get ahead; all in the doomed effort to get equal outcomes. The fact that the educated and affluent will either leave district schools or after school, so their kids will get more, is ignored, as is the fact that bright and motivated poor kids are the biggest casualties of the refusal to group by instructional need/level. Sigh

education realist said...

>IOW, if everyone cannot do it, no one is allowed; individual ability and interest be dammed!

No, don't be silly. The vast majority of kids in non-honors algebra can't do it, and the ones who can can barely do three step proofs. Meanwhile, they all need tons of algebra work, much more than they would have in years past.

I introduce algebraic/geometric proofs in trigonometry.

You are apparently ignorant of geometry's purpose in high school math. It's going to be gone in a few years. No one's getting robbed. I know much, much better than you do the needs of poor bright kids.

Katharine Beals said...

Gone for everyone? (Whose idea is that?) If true, that would be a real shame. Geometry proofs are a great introduction to proofs --for mathematically capable kids of all social economic backgrounds.

Anonymous said...

I am advocating for appropriately challenging material - in all subjects - for kids who are prepared for it, even if many or most of their classmates are not. EdRealist, why is this not reasonable?

I am thinking of the district mentioned by a regular commenter,where honors and upper-division courses have been eliminate and the kids who want them are told to go to a CC (at their own expense).