Disater lesson

Today I taught a lesson that was a total disaster.  I had my lesson plan and I knew all the standards I was going to teach to and I knew my objective and how I was going to assess it.  What I didn’t have that I needed was a script.  What I really needed was a 15 minute script explaining functions and function notation.  It was a meandering, disjointed ramble.  I had the key points I wanted to hit on my plan in  outline form but apparently it was too vague. It only took my CT a few minutes to make constructive criticism that allowed me a period of another subject to write a detailed script and saved the following two classes from my disaster.  I am going to always cue myself to consider a script especially for something new like function notation.

High leverage teaching moves meet the PPA.

This week two questions I had seemed to answer themselves.  The first was how to apply Seattle school district’s High Leverage Teaching Move number 3: Use of vocabulary.  The second was how to apply PPA 1E; when being observed during a lesson a candidate wants to be sure their lesson plan’s “learning targets are grounded in transformative multicultural knowledge, reasoning, performance skills, products, or dispositions.”  How do we accomplish this in math classes?  Trying to implement the Seattle School District call to provide students content and process terms daily is one way this PPA can be satisfied.  It is really important that in math vocabulary is used correctly.  For example slope is slope and teachers need to be sure their students are familiar with and fluent with this term.  This is not going to be as easy for someone whose native tongue is not English.  While English speaking students can to a certain degree intuit what slope is in graphic representations, non English speakers will find it difficult.   We need to make sure we take steps to make words like these clear to non English speakers.  This is a high leverage teaching move that begins to satisfy PPA 1E.

WBC (wrong but consistent)

At my middle school placement and now back at my high school placement I have been grading tests where problems build upon specific questions, such as slope.  What to do if a student miscalculates slope but then uses this wrong slope to continue calculations.  I adopted the notation "WBC" to mark the problem "wrong but consistent" and I give credit for consistent use of a wrong value.  This system does cause me concerns.  What if you switch the x and y coordinates when calculating slope, a simple mistake, and then I ask you to calculate your y intercept based on an equation using this slope?  In real cases this week I had kids do this.  The problem involved a line of best fit they had drawn so many were aware that the y intercept they were calculating was way wrong.  Some fudged the algebra to make it work, others simply offered the wrong answer, perhaps oblivious to the inconsistency of the two answers.  I wanted to give extra credit to the few who gave the wrong answer with question marks and arrows back to the graph.  I felt like these kids should get extra credit for their understanding of the inconsistency of their answer.  I think they demonstrated a real understanding of the underlying concepts involved.

Turn of phrase for interpreting slope.

I have been having a hard time walking students through a question we have been asking of them recently such as: “What is the real-world meaning of the slope” (of a specific equation).  We have often just mastered various symbolic ways of calculating slope.  My CT had a turn of phrase to help transition from a symbolic conception of slope to a language based description of slope.  Since the students know slope is rise over run it is reasonable for them to construct the sentence: “If you run 1 you rise y” or “for every run of 1 the slope says the y axis will rise ‘y’   By starting with these phrases you can build toward something like “For every day that passes Jan’s balance increases by $20.00.”  I think it is important to make these explicit connections from the symbolic definition of slope to an everyday understanding of slope.

Applying the distributive property when distributing a negative 1.

We started substitution for systems of equations today and the major hangup for students was the distribution of -1.  My CT had a turn of phrase he applied to this situation intended to guide students through the distribution.  He offered the strategy of thinking of a minus sign as meaning “Take the opposite of.”  Let’s say you are substituting the y value of (-x +2) into 2x – y = 5, resulting in the equation 2x – (-x +2) = 5. This is his turn of phrase which applies the “opposite” approach; “Think of the negative in front of the paenthesis as ‘the opposite’.  So ‘the opposite’ of negative x is positve x, ‘the opposite’ of positive 2 is negative 2.”  This should yeild 2x +x -2 = 5.  It is much smoother when you actually hear it said while watching him actually figure it on the doc cam.

High Leverage Teaching Moves, Strategy 2 Modeling.

When I am teaching I don’t want to offer the impression that I am some interlocutor handing down the mystical mathematical knowledge of the gods.  Rather I want to admit my position as a mere mortal like my students, who must work through problem solving just as they do.  I want to voice my thinking out loud, using phrases such as “I think to myself…” or “When I get stuck here I…”  By modeling the problem solving processes that I am using I want to encourage students that they can do the same.

High Leverage Teaching Moves, Strategy 1: Clear Teaching Point .

How am I going to implement the strategy of a clear teaching point?  What am I going to do so that I communicate to every student the lesson goal?  It should be explicitly stated, posted, and related to the standards.  In many good classrooms there are rituals at the beginning of class, warm-ups are typical.  I want to incorporate a ritual of stating and drawing attention to a posted lesson goal.  As a test I want to be able to start every post I make of a lesson to The Source with a statement of that lesson’s goal.  If a principal, parent, or clinical faculty asks me I want to immediately offer the goal and point out where it is posted.  This is the first of 8 high leverage teaching moves promoted by Seattle Public Schools.