How Would You Teach Algebra if You Only Had a Week?

LEsky85 on 31/05/2022 - 17:10
Last edited 01/06/2022 - 09:10

I am after suggestions on how one might go about teaching a subject like algebra to tafe students when I only have a week to get the information across. We are in the unfortunate situation that the course is written in such a way that it assumes students have learnt this stuff before, yet the reality is they may never have seen algebra before they get to my class (there are no pre-reqs for this qualification) or it might have been 20 years since they were in school (mature age students).

As an example the syllabus includes subjects like linear algebra (equations/line graphs/simultaneous equations/etc.), quadratics (factorisation method/quadratic formula/etc.), trig, geometry of basic shapes, interpreting data on a chart, etc.

In case it matters to you, the exam is multi-choice but they can't use a calculator. The pass mark is 75%. I do spend time on course discussing exam technique (eliminating incorrect answers for example if you can't get the correct answer, thinking critically about whether the answer they got makes sense, coming up with system to tackle each problem).

The main issues I see time and time again:

  • time management (only 75 secs allocated per question)
  • students too reliant on calculators in school and can't do stuff by hand, even basics. e.g. think about how long it's been since you did long division by hand
  • younger students never ask for help
  • You can't take notes or formula sheets into the exam
  • the course is reliant on having a sound knowledge of the fundamentals, so if you miss something early it will definitely sting later
  • society just hasn't done any favours for maths in that it's just not cool to be good at it
  • I can't change the course length or structure due to limitations with the regulator who sets the rules
  • In the context of adult learning, we are trying to foster the ability of students being able to think for themselves. We want to help as much as we can, but at the end of the day the qualification they seek relies sometimes on having the ability to find out things for themselves. They aren't going to be spoon fed out there.

Cheers guys and girls,

Esky

Edit: Qualification is CASA Licence for Aircraft Maintenance Engineering. Diploma of Aeroskills Traineeship.
Already like Eddie Woo / Khan Academy / Wolfram Alpha. They helped me when I did engineering maths at uni.

Education & Work

Comments

  • BathRobe on 31/05/2022 - 17:18
    +7

    Hey Esky - would definitely recommend watching Eddie Woo on YouTube. He single handedly taught me maths from about Year 9 onwards to much more complex topics.

    Maybe just watch it and take notes of what makes it clear for his students and how he phrases the subject matter. I think it’s important to get across that algebra is almost always a representation of something in real life. Sounds like a tough spot to learn in a week, but you seem to have solid plans. Best of luck!

    • HairyChickens on 31/05/2022 - 18:06
      +3
      Eddie Woo is the GOAT

      Keep in mind that e.w teaches the NSW syllabus for high school maths, but maths is maths and his delivery and how he gets you to understand maths rather than ROTE learn formulas is phenomenal.

      linear algebra (equations/line graphs/simultaneous equations/etc.), quadratics (factorisation method/quadratic formula/etc.), trig, geometry of basic shapes, interpreting data on a chart, etc.

      You can search these topics along with "Eddie Woo" and there are plenty of videos.

      • Esky85 on 01/06/2022 - 08:44

        Yep, I try to teach like he does. I like his style. Only problem, he has the same students for years, I've only got a week.

        I also like Khan Academy and Wolfram Alpha as others have suggested. I was just wondering if there were any others I'd missed. Sounds like this is going to be quite difficult for people whatever I do.

  • CrowReally on 31/05/2022 - 17:20

    plenty of free online resources (wolfram, khan academy etc) will have solved this question suitably. look at a few, find one that does what you want on the timeframe needed, direct them to it.

    alternately, solve for x.

    • Esky85 on 01/06/2022 - 08:47
      +1

      Cheers, been recommending those to people already but I still have people who struggle. You suggesting what I've already been doing has put my mind at ease a little that I am on the right track.

  • cashless on 31/05/2022 - 17:45

    Tell them to mind their P's and Q's

  • rektrading on 31/05/2022 - 17:48
    -2

    Algebra

    Any real-life use case?

    • whatwasherproblem on 31/05/2022 - 17:56
      +3

      I'm not sure about real-life, but you can use algebra to analyse graphs of things and extract trend/swing info.

      Such analysis could be useful when the graph is of the value of a tradable asset. You know, for example.

      • rektrading on 31/05/2022 - 17:57
        +1

        I think tradingview can do that. I haven't tried.

    • Seraphin7 on 31/05/2022 - 21:03
      +5

      Any real-life use case?

      (a) You buy 0.174 BTC at $50k and hodl for six days. At this time BTC is trading at $30k. What is your annualised rate of return?

      (b) Assuming this rate of return continues, how long can you continue to hodl until the bank sells your house?

      • rektrading on 31/05/2022 - 21:27

        Tradingview works out the PnL.

    • teacherer on 01/06/2022 - 09:41

      edgy

  • Switchblade88 on 31/05/2022 - 18:17

    What's the actual course? No point trying to teach algebra as a prerequisite if students are then going to be dependent on more than one week's worth of lessons from you.

  • SF3 on 31/05/2022 - 18:20

    algebra to tafe students

    Too late.

    Sounds like ✅ a box.

  • Quantumcat on 31/05/2022 - 18:38
    +4

    If they don't understand the whole concept of algebra at all there is no way they can tackle those topics in a semester. Algebra is introduced in like year 7 and then gradually built on over several years in school. I don't think you can go from not knowing algebra at all to solving simultaneous equations or solving quadratics in a couple of weeks.

    For what it's worth when I have taught algebra to bright primary school students (or older kids who don't quite understand it) I start with the idea of having apples on an old balance scale. There will be a basket with an unknown number of apples and the student has to keep the two sides equal to get one basket on one side and some apples on the other so they know how many are in the basket. So they can do things like take an apple off both sides, divide both sides by two (eg if there are two baskets on one of the sides), or take a basket from both sides (eg if there are two on one side and one on the other). We draw pictures of each step (of the scale and little apple drawings for each apple and little basket drawings for each basket). Having something physical in mind helps when they're gaining an intuition for whether performing a particular step will keep both sides equal.

    • Esky85 on 01/06/2022 - 09:26

      Thanks, this really helps. I also show the full working and I keep everything neat when solving equations. It's a constant battle. They might understand how to do simple equations but then if you make it one with a fraction they freeze, even though we covered fractions in the arithmetic section of the course and they had no problems.

      • Quantumcat on 01/06/2022 - 09:33

        Probably they are like a student I had, who was quite bright, but all through school he had figured out the answers through intuition/guessing and checking, rather than learning the operations you're allowed to do. When things got more complicated (ie fractions with things added and subtracted in the numerator and denominator) he got really lost.

        I think you're in for a tough time, as all these operations are learned one by one over years, with lots of practice and drilling in. When they're in year 11 or 12 they have a whole toolkit of possible operations they can use to solve an equation. If those operations are not second nature they're going to have a hard time. I think it would be like expecting a student to start writing history essays before they have much vocabulary, or know how to spell things, or have even been introduced to the alphabet

        • Esky85 on 01/06/2022 - 14:06
          +1

          You've nailed it. That is exactly what is happening. The course is meant to be revision, but I have to go back to first principles with about a third of my students which wastes a lot of the little time I have anyway.

  • garetz on 31/05/2022 - 20:50
    +1

    If you only have 1 week to live I recommend doing something else instead of learning Algebra.

  • mauricem on 31/05/2022 - 22:36

    How many nominal hours applied to the unit and again what course is it? Is Algebra a core unit or some not so bright idiot picked it as an elective. Is there any precedent of other years having a similar cohort passing?
    I've seen lots of stupid things over the 15 years I taught at TAFE but this is right up there!

    • Esky85 on 01/06/2022 - 08:42

      1 week (40 hrs). Diploma of Aeroskills. No, it's always been a crap course with lots of people who struggle if they haven't done it before but at the same time we get plenty of people who find it easy too.

  • shaybisc on 01/06/2022 - 08:42

    What's the course?

    • Esky85 on 01/06/2022 - 08:50

      It's the Diploma of Aeroskills leading to a CASA licence. Aircraft maintenance engineering. CASA set the syllabus. I'm stuck with whatever they say I have to teach whether we think it's relevant to their licence or not.

      • BewareOfThe Dog on 01/06/2022 - 11:04

        It's generally about using similar problem-solving skills, to what maybe used in the job.
        I was looking at doing Electrical late in life, but an electrician said don't worry unless you are good at Algebra and Trig.
        Mind you a lot of 50yo to 65 yo electricians don't strike me as 'bright sparks'

        • Esky85 on 01/06/2022 - 14:14
          +1

          This maths is never used in the job. Aircraft maintenance is meant to work on the premise that if there isn't an established documented procedure, you don't do it. Every task that you sign off has to have a manual reference in the corrective action. You are strongly encouraged never to memorise anything and always refer to the manual. Yet CASA wants us to teach maths but you can't use notes/calculators. Typical CASA there to serve passengers/pilots/…………………………………………………………………………………………………/maintenance in that order.

          • BewareOfThe Dog on 01/06/2022 - 14:52

            @Esky85: Crazy.

            I knew someone that used Trig in their job everyday (and they were not a teacher). They were a Surveyor.

  • Fexofenadine on 01/06/2022 - 20:58
    +1

    Practically, I would let all students know the week/s before that there isn't going to be enough time to cover the basics in depth, and that you recommend that they watch these videos beforehand (and provide them with your pick of what everyone's said above). In education this is called "flipping the classroom" as it allows you to spend the class time working through example questions rather than covering content.

    Ideally, if they're self-directed learners, this will happen, allowing you to focus on the content you require during that week rather than running around filling everyone's gaps.

    As Quantumcat said above it's not really going to be possible to get the deep understanding for those who don't get it now, but with the videos and your teaching you may (should) be able to get them over the line to pass.

  • bargaino on 02/06/2022 - 23:53

    It is quite possible to teach basic algebra in a week if you have smart students.
    However, if they are adults and do not know it already, it is unlikely that this is the case.

    As an example the syllabus includes subjects like linear algebra (equations/line graphs/simultaneous equations/etc.), quadratics (factorisation method/quadratic formula/etc.), trig, geometry of basic shapes, interpreting data on a chart, etc.

    Unless the exam is totally dumbed down, you might as well add number theory and quantum mechanics to the list. The best you can do is a refresher for those who learned all that properly in school.

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