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hi everyone uh today I'm going to be
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talking about study strategies that you
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need specifically for math-based courses
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and problem solving courses my name is
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Holly and I'm a learning specialist at
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Student Success Center at Concordia
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University
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so why do we need specific study
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strategies for math-based courses why do
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they why are they different from any
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other study strategies that you may have
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learned or practiced so far
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what we hear a lot from students is that
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there's too much content and not enough
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time to cover it all and so you want to
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actually maximize your study time
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the other thing that it allows you to do
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is to find out what is the most
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important part of the content and really
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focus your attention on that and learn
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that really well
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um
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the other complaint that I hear a lot
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from students is that they study
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something and they read it and then they
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forget it after two weeks so how do we
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use these strategies that help us uh not
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having to read over and over again
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something that we have studied just
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two weeks ago
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so what is this effective study
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strategies look like what we suggest is
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you do a bit of preview read a lot of
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solving and practicing and then do uh do
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some review at the end
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but basically how it works is that you
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do one bit of preview you read you solve
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what you have read you go back you read
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a bit more you solve you read back you
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and then you solve and then at the very
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end you review what you have done then
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you go to the next section again preview
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read solve and review let's focus on the
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preview section what do we mean by
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preview so previewing means that you
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look at the table of content you look at
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the big or bolded uh words you look at
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the titles and subtitles formulas
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definitions just to get the big picture
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to get an idea of what you're supposed
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to cover let me give you an example
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imagine if you have a bunch of clothes a
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big pile of clothes and you want to
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slowly go and take your red shirt out
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it's almost impossible if you have two
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pieces of clothes piling over each other
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okay so what we're going to do to help
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us find that red shirt for example or
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pair of jeans that we want is we have to
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shelf or close it previewing does the
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same thing for us so imagine if I want
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my red shirt I can easily find my red
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shirt in this closet when I preview I
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create shelfing in my brain and what it
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does is that that shelf might be empty I
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may not have content in it yet but once
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I learned the content I know where to
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place it and that's how it helps me
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learn in a more organized way I'm
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basically organizing my brain when I'm
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doing a preview
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the other thing that it does the
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previewing does for you is that it
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allows you to learn about the content
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that you may be missing and you need to
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know for that specific class so
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um as we know problem solving content
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are very cumulative it means that if you
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are
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um not mastering chapter one you will
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have difficulty learning chapter two
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right because they're they're built on
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top of each other
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um
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it's the same things it's the same thing
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when we are
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um learning let's say algebra learning
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calculus you need to know the foundation
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of each course before you can move up
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right so when you do preview
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if you come across something that you
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feel you haven't learned well and your
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next class is going to focus on that and
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it requires you to have some kind of
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foundation for that course it helps you
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to go and learn it before you go to the
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class do you know sometimes we go to the
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class and we we're a bit lost because we
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haven't seen uh the content before or we
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feel like we should know this but we
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don't know this so it helps you really
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brush up on your background knowledge
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making sure that you have solid
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foundation before you move on to the to
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the next class or to the next course
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the other thing that it does is that it
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takes your attention and focus it in the
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class A lot more let me give you an
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example so imagine if there's a level of
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noise happening outside your room okay
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and then all of a sudden with the same
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level of noise someone mentions your
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name your attention immediately goes to
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that voice right it's automatic you
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don't really have to think about it
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we're trying to create the same thing in
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our brain by previewing because when you
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have created that sort of familiarity of
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course not to the level of your own name
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but some level of familiarity with the
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name of the topics that are about to be
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covered in your class what ends up
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happening is that when the professor
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mentions that your attention immediately
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goes to that right so a lot of time I
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hear from my students that I sit in the
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class I'm trying to pay attention but I
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constantly get lost and I'm confused or
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I start daydreaming so there are a lot
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of different reasons for that preview
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can help I'm not saying that it's going
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to solve all the problems there are so
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many different reasons for that but uh
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for being lost or confused or or
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losing your attention but at the same
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time it can in some cases in a lot of
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cases help you stay more focused
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so
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I'm hoping that I've given you enough
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reasons to do the preview because
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the preview is supposed to take maybe 10
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minutes 20 minutes maximum half an hour
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unless you're fundamentally missing uh
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content
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um from your previous knowledge
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otherwise it should not take very long
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but it keeps you focused it gives you a
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sense of foundation a strong foundation
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and more preparedness to go to the next
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class
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in addition to all of that if you are in
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a class you know how sometimes we're a
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bit insecure feeling that I have a
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question but I'm the only one who
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doesn't know that content so I'm not
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going to risk it and I'm not going to
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make my professor know that I don't know
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what I'm supposed to be knowing when you
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do preview you have more confidence to
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ask
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good questions relevant questions if you
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are focused if your background knowledge
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is solid if you are paying attention in
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the class and you're following what's
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happening in the class
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and if you're still having a question
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chances are 50 of the rest of the class
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have the same question but there are two
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uh they're not confident enough to ask
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the same question so you can confidently
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ask that question and not let that stop
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you from learning further in that class
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okay
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so we talked about the preview
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let's see what happens after that so one
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of the things that I ask students when
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they come to see me and they say they
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have difficulty learning in their
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problem solving courses that how do you
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study so that's my first question how do
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you study so there are different
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strategies but some of the actually
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really good students tell me that when I
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go home right away after my class I take
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my assignment and I look at the
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assignment and I solve it how do you
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solve it I go back to the content I find
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what's relevant I read over it I bring
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it I write it I go back I take what's
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relevant I bring it I write it I go back
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what's relevant I bring it I write it I
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finish the assignment I hand it in I get
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an A plus in all my assignments I go to
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the exam I blank I panic I fail
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so what happens
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what actually these students have done
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here is that they got really good and
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assembling p in assembling pieces
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together they did not get good at
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making the content
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right or solving that problem they can
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put pieces together but they're not
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actually learning right so let's look at
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how it works
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we did the review now we're going to
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talk about what happens in the read and
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the solve section right so
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this is what you're supposed to be doing
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imagine you're trying to read chapter
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three and study chapter three you go to
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section
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3.1 there is a bit of content
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you skim through it you don't have to
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stay on it forever you skim through it
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you get to the first example cover the
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example cover the solution
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look at the example
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try to do it on your own try for like
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three minutes five minutes max if you
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get stuck
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read it again try to analyze the
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question try to make sure you really
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understand the question if you're still
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not able to solve it look at the
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solution remember this is still the
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example that is inside the content or
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your PowerPoint or your textbook or your
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ebook right look at the example and uh
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and and and try to to learn from what
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has happened in the exam a lot of
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students read over the example and they
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think okay my job is done I've learned
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this I'm good I'm good to go
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but in fact
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you're only
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you only have learned the content when
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you're able to apply the content in a
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new context what does it mean you see
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the content here these examples are the
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new context for that content so unless
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you're able to solve these examples on
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your own
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you haven't really learned it not
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without really Peak at it or checking
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the formula once you're able to do all
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of them without the help of the textbook
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or your ebook or whatever resources
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videos internet whatever it is that
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you're using that's when you have
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learned it okay so we look at the
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content we cover the solution we try to
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do it on our own if you can do it
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perfect if you can't do it you look at
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it you learn from it you ask yourself
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and this is the key part this is when
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you know whether you have learned it or
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not
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you ask yourself what was it that I was
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missing
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in being able to solve this example why
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was I not able to solve it was it lack
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of understanding of the content was it
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not remembering the formula was it uh
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misunderstanding the question was it a
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miscalculation a simple miscalculation
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there was a question I forgot
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um or like I didn't use my um
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calculator properly or
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it you have to find out why you made
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that mistake or why you were not able to
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solve that example and that's the key
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part because you're not going to make
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the same mistake again right then you go
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to the next bit of the content you do
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the same thing look over the content get
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to the example cover the solution try to
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do it on your own if you can do it
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perfect if you can't find out what part
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of it you were missing once you know
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what you didn't know that's when the
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learning is happening it's starting to
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happen now how do you complete that
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cycle of learning once you get to the
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end of the section not to the end of the
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chapter to the end of the section
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you go to the end of the chapter and do
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some problems that are relevant
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to that section don't wait until the end
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of the chapter by the end of the chapter
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you've brought in so much content to
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your brain that is hard to dissect
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what's relevant
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you want to strengthen what you've
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learned first and then you want to move
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on to the next bit right so you get to
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the end of the section you go to the end
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of chapter you do problems you do the
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beginning of the problems
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um some problems in the beginning of the
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end of chapter
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if you see it's too easy you move down
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you could also start with some problems
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in the middle
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and if it's too difficult you go back up
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usually they're ordered in the by their
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level of difficulty if you see they're
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too easy you go uh to
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um later problems in that section
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okay
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once you did a few of the end of chapter
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problems then you go to the new section
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you do the same thing all over again
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content example cover the solution find
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out where you've made the mistake and
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then you go to the end of chapter
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problems and you do a bit more the
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benefit of doing that is that is that
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you're strengthening your knowledge step
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by step and it helps you at the end of
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the chapter to go back and do a full
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review of everything that you've done do
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some problems that are related to all
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the content the chapter together and you
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make sure that you have a stronger
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Foundation
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okay
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sometimes you need to do uh more of a
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space practice like you finish the
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chapter today and in in a couple of
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weeks go back and do a few problems uh
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what you have learned because remember
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when you're studying one chapter you are
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dealing with let's say five formulas
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right
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um and so you know there's a limited
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number of formula that you are applying
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in your problems a couple of weeks from
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now you've studied three more chapters
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for example so now the pool of the
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formula that you have to deal with
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is like 20 formulas
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so what you want to do is instead you
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want to make sure that I'm able to go
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and choose what's relevant to this
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problem and apply it there
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okay so that's what we call Active
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Learning in problem solving courses if
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you are in lower level courses like
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pre-cal Cal 1 Cal 2 even you are you
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have less content and more examples and
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more practice problems once you go to a
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higher level of courses you have more
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content and the application of the
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content in the example becomes more
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important in your 300 level courses
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in your 400 level courses in your
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graduate course
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okay
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we often hear a lot about note-taking
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so
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what does it mean to do note-taking in
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um a problem solving course of course we
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have a bunch of workshops and there are
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lots of videos that you can find on the
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internet on note-taking I'm not going to
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focus on General note-taking methods
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which you can find and it applies to all
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sorts of course courses I'm going to
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talk about the specific note-taking that
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you need for
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um
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a problem solving course and that's how
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to create your formula sheets so a lot
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of time people say well we have a
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formula sheet in the book or the the
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professor gives us a formula sheet or in
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the exam we have access to the
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formulation okay we have a cheat sheet
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or we have a formula sheet or we can
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create one how do we create your formula
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sheet this is basically what you put in
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your formula sheet name of the formula
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the actual formula
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you might find it useful to have an
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example of that formula
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but if you are again in lower level
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courses that's where it ends right so
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for example I'm trying to do a
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derivative of a power function
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I write the formula
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I have an example that gives me enough
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information for what I need to learn in
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count one
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okay once you go to higher level courses
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they're not going to ask you do the
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derivative of this function
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they're going to ask you for the
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application of that formula formula
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calculate the rate of change
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and you need to know which formula that
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requires which formula does the rate of
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change require
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okay so this also gives you a good tool
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for practicing for the exam as you go
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further to the course you will do more
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and more of this practice and you
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require less and less referring to this
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formula sheet
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also you may decide to for example cover
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the formula and just look at the
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application and say what's the formula
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for a rate of change what do I have to
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do I have to do the derivative okay so
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now that I know that I'm good I can move
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on to the next bit right
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if there are formulas that you can
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derive from the original formula don't
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write them all here unless it takes you
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half an hour to derive the new one if it
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is something that takes you
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30 seconds do not make this too crowded
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okay you you wanna you want your formula
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sheet to be useful to be able to find
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stuff in it so if there are things that
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you know already you don't need to put
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them here this is only for things that
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you feel you either don't know you're
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learning new or you may forget hopefully
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over time you will need less and less
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um
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referral to this formulation
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okay
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that brings me to the next bit of this
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uh video which I'm going to talk about
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we've talked about how to uh to
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generally approach your problem solving
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courses the study strategies that are
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required for problem solving courses
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but this part I'm going to talk about
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the steps that you have to take when
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you're actually solving a problem
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the content of this comes from a book
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called How to solve it from George polia
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George polio is a mathematician that
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claimed if you follow these six steps
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into any problem in your life you would
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be able to solve it I think that was a
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bit of a stretch but I know for sure
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that this does work for uh problem
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solving courses
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so
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what's the first thing that I do when I
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get a question in math and this is you'd
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be surprised how many students miss this
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step you read the question
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and then you read it again this is the
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most important part of uh your
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problem-solving strategies
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a lot of us when we see a question we
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see it we don't read it we immediately
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go back to our brain we try to find
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similar questions and we try to write
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and think about the formula that is that
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is related to this you don't want to do
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that what you want to do instead is you
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want to read the question once
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to get the big picture then you want to
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read it again to make sure you fully
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understand the question okay you want to
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highlight what's important or underline
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what's important you want to pay
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attention to what the information is
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giving you and what is what the question
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is giving you and what it's asking from
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you list them
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you may need to uh
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analyze the question in a way that you
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divide it into smaller sections
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okay
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and then analyze it bit by bit and then
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put them all together and then list what
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it's giving you and what it's asking
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from you once you do that you need to
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think about a way that is going to take
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you from what's given to what's being
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asked for right so
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you might decide to make visuals if
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possible for your type of questions
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then think about a plan
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use all that is given
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and think about how you what are the
00:21:50
steps you're going to be taking to get
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to what is being asked for
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once you think about these steps that's
00:22:00
when you translate this problem into a
00:22:03
mathematical equation or a series of
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equations that is necessary to solve
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that problem
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once you get to this stage and remember
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this is often where people start from
00:22:16
they think about okay what is the plan
00:22:18
and through that a lot of times we we
00:22:21
miss details this becomes more and more
00:22:24
important as you go higher in your
00:22:26
courses because in again in lower level
00:22:29
courses
00:22:30
the the type of question you're being
00:22:33
asked is a very
00:22:35
um standard
00:22:37
in higher level courses they give you
00:22:39
similar questions to what you've seen
00:22:41
but they change a small bit in it
00:22:43
and that small point is what makes all
00:22:47
the difference in the content in the
00:22:50
solution that you're going to use
00:22:54
once you have your system of equations
00:22:57
solving is usually uh the easier part of
00:23:01
it
00:23:03
once it's done you want to check your
00:23:05
solution
00:23:07
uh
00:23:08
checking your solution can be done in
00:23:10
different ways sometimes you use
00:23:12
mathematical ways to check your solution
00:23:14
sometimes you for example like back
00:23:17
substitution sometimes you may use
00:23:21
um just take yourself out of
00:23:25
the math of it and see if that question
00:23:28
makes sense in real world for example uh
00:23:32
if I am calculating a budget of uh a big
00:23:38
size company with
00:23:41
um 3 000 employees and if their annual
00:23:43
budget comes to
00:23:47
of I don't know twenty thousand dollars
00:23:49
then there's a problem then I've made a
00:23:52
mistake somewhere so I can go back and
00:23:55
fix that mistake find that mistake and
00:23:57
hopefully fix it
00:23:59
okay
00:24:03
that brings us to uh the end of this
00:24:07
video I hope that you have
00:24:10
um that has answered some of your
00:24:12
questions
00:24:14
um if there are more questions or if you
00:24:17
have comments please contact the phone
00:24:19
number
00:24:21
um and we would be happy to hear from
00:24:24
you thank you very much and have a
00:24:26
wonderful day
