WEBVTT

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[Music] Welcome

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to Helping Struggling Learners

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in Algebra.

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My name is Sally Collins,

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I'm a Math Teacher

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at Castle View High School,

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here in Castle Rock, Colorado,

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and we are a member

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of the Douglas County School System.

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I believe one of the biggest hurdles

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that students face

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when they learn mathematics

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at any level is what they perceive

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as their own ability to do mathematics.

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But what I find most

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with the struggling students is I have

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to create a situation

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where they feel confident,

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where they feel safe,

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where they are willing to take risks,

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and that's a tough thing to do

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with students who have typically not

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been successful in mathematics.

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The foundational skills

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that students lack

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that often make it difficult for them

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to learn algebra is a general conceptual

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understanding of numbers

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and of the operations that happen

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on those numbers.

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While they may not be as efficient

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as some more successful students

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or be able to do it as quickly,

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they are still capable of being able

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to understand conceptually what's going

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on and actually do some

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fabulous mathematics.

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Types of activities that I might use

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to help students learn concepts

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typically revolve

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around contextual problems.

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When we teach linear equations

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and the graphing of linear equations,

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we typically do a lot

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with presenting slope

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as a constant rate of change.

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The lesson that I did today had a lot

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to do with calories and the burning

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of calories at a constant rate,

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and then that was translated

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into linear equations.

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We teach inverse proportions by talking

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about oil spills and the depth

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of the oil spill versus the area

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of the oil spill

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and having a constant volume.

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We teach quadratic equations

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when we talk about launching missiles.

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It is impossible to teach in context

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without somehow crossing

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over into the other genres

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of mathematics.

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There are elements of geometry,

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there are elements of trigonometry,

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and there are elements

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of algebra inherent

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in every contextual problem.

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So, the beauty

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of it is it shows the students

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that mathematics is not a set

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of isolated skills that you practice

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and do and master.

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But it's actually problem solving,

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and the skills are what help you

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to become more efficient in the solving

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of the problem.

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In terms of linear equations

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and graphing linear equations,

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a major misconception is just the

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understanding of what an x-intercept is

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versus what a y-intercept is,

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and how those relate

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to what the equation represents.

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When you present a problem in context,

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it's almost impossible

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to misinterpret what the y-intercept

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means because it has meaning in terms

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of the problem.

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However, when I give them a problem

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that has no context,

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and so it's just a equation

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where I ask them to identify the slope

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and the y-intercept,

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that's when my students have the biggest

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problems and where they make the most

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mistakes and where they flip-flop the x

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and the y axis and start graphing off

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of the x-axis rather than the y-axis

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and put slope incorrectly as run

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over rise rather than rise over run.

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If they have context, however,

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it doesn't make sense to do that,

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so they rarely make that mistake

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if it's done in context.

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I also do a lot of scaffolding,

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particularly with my

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struggling students.

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Scaffolding to me means

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that I introduce a skill,

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introduce a concept

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at a very basic level,

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practice that until I know

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that they understand that

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and then add a twist to it.

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I continue to add different layers

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of complexity and different layers

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of understanding each time I do it.

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The best way, I feel,

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to be able identify students'

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misconceptions

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when they are learning any mathematical

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topic, but particularly algebra,

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is through the use of discussion

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and group work.

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It's easy to follow a process

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and be able to mimic a process,

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but when you have

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to describe what you are doing

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and explain what you are doing to those

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around you and defend what you are

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to those around you,

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that's when misconceptions become

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inherently apparent.

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In terms of what type

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of questions do I ask in order

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to determine whether students are

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grasping essential learnings,

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it's almost always an

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interpretation question.

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Tell me what that number means;

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tell me what that represents

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in this problem; explain to me why

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that number is negative in this case,

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why is the graph going down?

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Why is the y-intercept what it is?

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What does it mean in terms

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of the context of this problem?

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One of the ways that I work

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with my struggling students to make sure

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that they continue to stay focused

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on what it is that they are doing,

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is I want them to do a lot

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of work in groups.

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I find most students get off task

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when they are incapable--

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or they think they are incapable--

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of being able to solve what the

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problem is.

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I have to make sure that,

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when I set them up into a situation

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where they are doing group work,

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that they have the ability to be able

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to successful.

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So, there has to be enough background

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knowledge, there has

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to be enough teaching prior to that,

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there has to be enough practice prior

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to that, that when I give them a fairly

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rich problem they have the ability,

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they have the knowledge,

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and they have the capacity

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to be successful in it.

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Even if they are not exactly sure how

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to get there, they know

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that they can talk with their group

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and be successful in it.

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That's when they continue

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to be persistent and pay attention

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to what they are doing and don't wander.

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The way I develop persistence

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in my students

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for learning algebra is directly tied

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to the way that I grade.

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There is a big difference

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between being able to do the mathematics

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and get the grade that you want

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versus truly, truly understanding what

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it is that you are doing in the algebra.

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But I want the grading system to focus

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on their level of knowledge,

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not on the amount of work

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that they have achieved.

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So, my class is designed

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with my standards-based grading

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for students to have multiple

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opportunities to go back

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and rework problems

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and relearn concepts,

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and show me that they have learned it

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again in order for them to attain

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that particular standard of Meets.

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To learn more about Helping Struggling

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Learners in Algebra,

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please explore the additional resources

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on the Doing What Works website.

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[Music]