Authentic Engagement with Mistakes

One question I've been grappling with a lot this year is trying to help students authentically engage with their own mistakes and misconceptions. My first year of teaching I was the queen of corrections, letting students correct every test and quiz to try to realize what they did wrong and learn from it. My middle schoolers were generally very honest about this, but when I switched to high school I saw the huge desire for good grades outweigh the desire to learn from errors. I saw more and more cheating and less and less studying for the initial test and I cut it off. 

I know there are such huge payoffs for kids who learn to analyze their own mistakes, though!! And telling a student who genuinely wants to learn from what they did wrong and is proud to demonstrate to you that they've mastered a concept that they are out of luck? It makes my stomach turn! 

This is very much a first draft, but here's what I'm thinking....

Things I'm considering:

• Only allowing students to re-test on a set number of assessments per semester (2....3....suggestions?). This allows the opportunity to make up for a "bad day" but not get used to failing the first time and making it up the 2nd time around. Does this go against the whole idea of always being able to learn from their mistakes? 
• I only want to offer 1 re-test....what if a student in genuinely absent? Do you start making exceptions?
• About 1,000 things I haven't even thought to worry about yet

Has anyone come up with a system they really love for allowing students to learn from their mistakes and prove mastery without sacrificing the high expectations on the first assessment? 

Back At It

THREE YEARS AGO: I was a 2nd year teacher at a private middle school in a very affluent area. I lived in a new city 2 hours from my now husband and 12 hours from all my family and friends, was the youngest person on my staff by at least 30 years, and had a whole lot of free time....which I filled with school work! That's where this blog was born and, for a while, actually thrived. I was working 90-100 hours a week and it generally wasn't a very balanced life. Something had to give (Spoiler: it was the blogging!).

TODAY: I'm starting my 5th year of teaching and my 3rd year at the school I moved to when I decided to finally be near my aforementioned husband. I fill my days with much more balance- teaching in a STEM magnet program, piloting a blended learning class for our district, tackling AP Calculus for the first time, satisfying my dog's desire for an infinite quantity of adventures, and enjoying being in my late 20's with an amazing husband and group of supportive coworkers and friends.

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After a 3 year hiatus, I'm working on getting back into blogging. I am excited to build my PLN and share ideas with a supportive community worldwide who share the same passion that I do- designing activities and curriculum to make math exciting and engaging for our students. 

Consider this post a bridge between these 2 phases of life....

• Post before this (some of which have been deleted....because gosh I was bright-eyed and overly excited about every moment of my day) are the thoughts of a young, excited teacher who has lots of autonomy, no standardized tests, and is still learning exactly what good teaching looks like to her.
• Post after this are the reflections of a (slightly) more seasoned teacher who believes that the students should be in the driver's seat in their own education, that experimentation and failure are a good thing, and that I still have a ton to learn! 

Let's get mathy, y'all! 

One of Those Days...

I've been watching way too much Keeping Up With The Kardashians in an effort to numb my brain during end of quarter grading, so here it is, the peak and the pit of today.

Pit: The server goes down. In the middle of 5th period. For 2 periods. When I have tablet and Smart Board activities planned for all! Coworkers lost all files. Thank you, Dropbox, for saving my life. 

Peak: My Geometry class bringing a staples "easy" button to class and it exclaiming "That was easy!" every time we successfully finish a tough problem. Special right triangles ain't never been so much fun. 

Notice...the peak is the kids. The pit is all the other nonsense. 

Everyday

The most important thing I've learned as a teacher is this:

It is just as important that I learn something new every day as my kiddos learning something new.

This year a new teacher was added into our middle school mix....a wonderful, talented, dedicated teacher who uses her humor to inspire her students. She had previously been working with much younger students, but her certification was in MS math and science and she was called upon to fill a role when we fell one teacher short. She has faced a harsh backlash...mostly from parents who thought of her as an "elementary teacher" and were upset their children didn't have me, the usual MS math teacher. 

But, despite the challenges, I have seen her rise to the occasion and I am so happy she did. I have learned so much about inquiry teaching for her, coming from her science perspective.  I'm feeling particular inspired by her approach to slope right now. No rise over run here....just graphs of proportional relationships in real life and unit rates. These were ideas I grazed before, but she dove in head first and never let the students see an "equation." Yes, this tactic has its drawbacks. But striking a balance between that extreme inquiry and the old school "practice, practice, practice" that stubborn math teachers have held so dear is really where my philosophy of education has settled. I love having a colleague to look to for inspiration and to challenge the way you had previously done things.

There is nothing like the challenge of teaching to keep you an eternal student.

A Geometric Valentine's Day

We're just digging into geometric mean in Geometry and the inevitable question of "Why are there 2 types of means?" always arises. 

Here's a timely explanation of one way math & geometric mean are used in real life....just in time for Valentine's Day!

Happy Valentine's Day to all of you!

Update: Discussed this with my class last period...they immediately wanted to know if I used eHarmony or Match.com (despite the fact that they know I'm in a long term relationship) and which was better. They decided they should probably test both to figure out which one worked better.  I guess I'm glad they're trying to test their conjectures? Scientific thinking at its finest. 

Mathematical Bakery

Working with generalized proofs today, we ran into a problem that said (a+b)(a+b)...we were using the distance formula. Oh the crazy answers I heard from my Geometry students!! Sure, we haven't done a lot of multiplying of binomials this year, but still....I was a bit frightened. I explained to them that at the end of this year we're going to do a pretty hefty Algebra review to make sure they're in shape to take Algebra 2 next year. I told them "factoring is cake compared to what you'll see there!" The following conversation ensued:

Student 1: "So....you're saying Algebra 2 is like a scone?"

Me: "What??"

Student 1:" Well if factoring is cake, Algebra 2 is a scone....it's a little harder."

Student 2: "Pre-Calculus must be like a stale scone!"

Student 3 (from across the room): "And Calculus is like a really hard loaf of bread!"

Student 1: "Good thing we have studying...that's our coffee! We can dip our scones into it and it will soften them and make them taste better."

Student 3: "I don't think I'm going to study in Calculus."

Me: "Why not?"

Student 3: "Because....old bread dipped in coffee? Gross."

Groups of kids like that remind me why I love my job, especially on the days when you're ready to hide under your desk.

Just a normal Monday night....

Most people spend their evenings catching up on HBO shows, eating leftovers from the Super Bowl, & doing recreational proofs, right? 

That's what I thought.