Forget-Me-Not-So-Soon

I get very frustrated when trying to help students work through algorithms when they have difficulty recalling prerequisite information.  For example, when helping a student determine the y- and x-intercepts of a function for his Precalculus homework, I asked him what 9 divided by 0 means.  He said that it is equal to 0.  When I reminded him that division by zero is undefined, I could tell that he felt stupid for having forgotten.  It is never my goal to shame students, but with all the responsibilities that go along with teaching, we simply do not have enough resources (time, energy, patience, ideas, student persistence, etc.) to be able to guide students through rediscovery or tie up loose ends in comprehension/meaningfulness of the content.

The effects of tests on learning and forgetting have been studied at length since Ebbinghaus introduced his model for how we retain (and fail to retain) information.  It is suggested that in a typical schoolbook application (e.g. simple knowledge or algorithmic skill), most students remember only 10% after 3–6 days (depending on the material).  Repetition of material increases retention by increasing the height of the curve:

However, we rarely have time for such intensive remediation in the classroom.  Can testing itself be a way for us to utilize the benefits of active recall?  If so, how should these be framed and structured to best benefit our students?  Feel free to ask questions and comment below as we generate ideas on this.

The Effects of Tests on Learning and Forgetting

Notes in Class

In one of my grad school classes we are discussing the materials to compile for the hiring process and for our own professional development, such as the professional (and the working) portfolio.  I liken the portfolio to the senior project of a music performance degree candidate.  Each have both visible components and active components.  The written composition (lesson plans, etc) can be performed by another, but the individual performance of the material is also a basis for assessment.  If even a highly-skilled individual chooses a format or material that is inappropriate for their unique situation (personal strengths, student needs, specific concepts, their instrument) their “performance” may be sour.  Likewise, even the best-laid lesson plans or an idiot-proof piece of music in the wrong hands can be ruined.

There is no one-size-fits-all style of teaching.  That is why "style" is such an appropriate word for what we do.  We must constantly reassess and refine our style as we progress, mature, and get different students with evolving needs so that we do not become teachers that just go through the motions because we already know how to play the notes.  To lose our passion and our own desire to learn, to refine teaching methods, to better understand student needs, and to build up others in the profession would be to lose the magic behind the music.  Teaching is more than mastering content and methods, just as much as music is more than notes on a page.

A neat describing some of the mathematics behind perception of musical beauty and dissonance.

and 

a video showing the connection as it relates to more specific physical factors.  Gosh, I love math.

Home Teaching

Westlake High School, 15 August 2013: professional development day.

Nothing says "Welcome home" like a table full of candy bars and a sign reading "Grab your favorite." Except perhaps a sign that actually says "Welcome home."

My transitions from substitute to student-teacher, from California to Utah, and from working a multitude of part-time jobs to fully focused on math education have all had their ups & downs thus far. This transition from summer to school-year has come upon me so quickly, I have had little time to sit down and reflect on this amazing experience.  That's part of the beauty of a full life - words hardly do it justice.  The hectic nature of a teaching career, especially at the start of a new school-year, cautions me to strive for balance with renewed (and facetiously restrained) vigor.  I do not fear that I will forget the lessons I am learning; my fear is that I will lose the perspective in which I learned them.

Teaching is more than a profession, it is a way of life.  Along with it comes a life's worth of lessons that I will want to share.  Part of the goal of critical reflection (whether self-imposed or assigned) is to give the learner a tool to process teachable moments and extract the lesson.  Later on, however, I may need to be reminded of what I learned or experienced.  Of course, these lessons may benefit my students and peers, but today I remind myself that critical reflection is not a chore; it is personal development.  It's a good thing I love to learn.

Adapting Mathematics Instruction for ELLs

Misunderstanding the language-concept connection by math educators attributes to low levels of achievement among ELLs, thus widening the gap, so to speak.  This research discusses parallels between effective mathematics teaching and effective second-language teaching, as well as specific strategies that both use to make input comprehensible.

Garrison, Leslie and Mora, Jill Kerper.  Adapting Mathematics Instruction for English Language Learners: The Language-Concept Connections.  Changing the Faces of Mathematics: Perspectives on Latinos (March 1999): 35-48.

Radio Reading

Radio Reader script (3 students)

Full text of the article: "To see but not to read; the magnocellular theory of dyslexia"

Word-attack strategy visual aid used in the activity was taken from:

"Animal Crackers and Apple Juice"

Radio Reading strategy taken from:

Tierney, Robert J. Reading strategies and practices: a guide for improving instruction. Boston: Allyn and Bacon, 1980.

A one-page summary of this strategy from Western Michigan University

To create your own Prezi online presentation:

Register at Prezi.com with your .edu or school district email address to get a free "Edu Enjoy" account - a step up from the public account.

Watch tutorials and be amazed.

Create.

Engage.

Giving Math a Voice

"As a kid, I felt that my voice was a little stifled."  Many kids love to socialize.  When I was in high school, one of my classmates regularly requested "social breaks" just past the halfway mark of our 90 minute blocks.  Though we laughed it off as a joke at the beginning of the year, we began to echo her call for breaks in the intensive curriculum (we were in health care professions track classes) to decompress and let our brains recover from technical information processing and critical thinking.  Little did we realize, many of the real-world topics we discussed during our free time could have been associated with themes and concepts we encountered in the classroom.  All that was needed was context and perspective.

In his talk on math education at TEDx Providence, Khalil Fuller shares his own experience helping his peers relate to math in high school.  He saw a glimmer of hope when math seemed like it could be fun.  His inspiration: Kobe Bryant.  More importantly, how Kobe Bryant and other basketball players created data that students already knew and even understood.  They heard about it on the radio, on the news, and most ostensibly on ESPN.  "Was that the exact kind of conversations that students all around the country are having every day and just overlaying math on top of it?"

Math Hoops and the organization that got them started, Big Picture Learning, are examples of educators that are working to understand what students are passionate about and tap into that in the classroom.  Though Math Hoops is still in the developmental phase, it may be worth keeping track of as a possible tool for future use in math classrooms around the world.

"The world is a fascinating and fun place.  Shouldn't the classroom be, as well?"

Watch the full video from Khalil Fuller at TEDx Providence:

A somber footnote:
"...in a major study in a U.S. city they found that 94% of murder victims under the age of 25 were high school drop-outs.  Literally bored to death."  Keeping in mind that correlation does not equal causation, this still strikes me as a disturbing correlation.  I love keeping the classroom light-hearted, but it is important to remember the gravity of my task and the responsibility of youth development that remains in any classroom.

Writing to learn (WTL)

Grad school is the best.  For my "Content Area Reading & Writing" class, I researched WTL and presented the strategy to the class.  Not only do I love the philosophy behind WTL, but I now love Prezi (the online presentation format) as well!  Here are a few of the resources I found online:

What is writing to learn?

Writing Across the Curriculum: Mathematics

Mathletically Yours,
Ms. Berg

Literacy & Mathematics: The Teaser Trailer

At the start of this cycle of summer classes I figured my classes wouldn't lead to much material that would transfer directly to my own classroom since both of the courses are language-related.  After all, math is heavily reliant on symbolic expressions, graphs, and conceptual understanding - that makes math "culture-free" and it doesn't change with language, right?

TEAL 6310 (Content Area Reading & Writing) deals with advancing literacy in the classroom and TEAL 6770 (ESOL Instructional Strategies in the Content Areas) discusses tools to make content comprehensible for English Language Learners (ELLs).  Much to my surprise, each syllabus included a Unit of Study within our specific content-area (of which mine is obviously secondary mathematics) consisting of 4 successive lesson plans that incorporate the principles we were to learn through the course.  Okay, so there was obviously a direct connection to the classroom there.

With each successive project, however, I am finding more and more connections between literacy, language, and how we teach math in the inclusive classroom.  For the sake of brevity, this is as much as I will disclose today.  Consider this a teaser trailer of the Literacy Chronicles (not to be confused with my heretofore unexplored territory in the Numeracy Chronicles) and what connections I am able to draw between the classes I have taken and the reality I am experiencing.

What up with Spectator Math?

Amy Benjamin

Mathletically Yours,

Ms. Berg