Plurk

212 responses to this plurk (Jump to bottom)

  • mindelei thinks
    they need to learn how to do it all by hand...then the shortcuts. (I know, not making your job any easier.)
  • JackieB
    Why do they need to solve complex equations by hand?
  • budtheteacher
    How many of them will actually use that later? Like, for really real?
  • mindelei says
    I just think you should know how to go about doing it without the tech.
  • mindelei says
    It's the same way when I learn how to use a program, I want to know the long way around through it before learning the shortcuts.
  • mindelei says
    Then I know how to use it better. But, hey - that's just me.
  • JackieB
    Why? How is it "better" to be able to solve it by hand than using a graphing calculator or a CAS program?
  • mindelei says
    It's not really about "using the equations" it's about learning to think through a problem.
  • mindelei says
    I'm not an advocate for memorizing equations - they're in reference books. But I think kids need to learn to think their way through math.
  • JackieB
    How does using tools (CAS, graphing calc) prohibit problem solving? I think it makes higher math more accessible to more students.
  • JackieB
    I'm not trying to be contrary here, I really want to know.
  • mindelei says
    It's about building on the basic knowledge that can be expanded by the use of tools. Plus, these skills transfer to...
  • mindelei says
    higher thinking and reasoning skills.
  • mindelei says
    I'm not saying you shouldn't use the tools, I'm just saying they need to know how to think things through which will allow them to use...
  • mindelei says
    the tools to their advantage.
  • budtheteacher
    mindelei - Do they? I had someone push back at me on that lately, and it's put me in a weird place.
  • milobo says
    Students need to know basic skills as building blocks so they can understand higher concepts.
  • budtheteacher
    I'm all for lots of thinking - but there're plenty of practical and real problems requiring solutions.
  • milobo says
    We wouldn't say that because we have books on CD (or iPod) that kids don't need to have reading skills, right?
  • budtheteacher
    Math problems in a book that have already been answered might not be the best problems for our kids to be looking at.
  • budtheteacher
    Would anybody here disagree that kids need "basics"? The trick is - what're the basic tools/concepts?
  • JackieB
    But if your "goal" is to solve an equation, why not just use a graph or CAS? If your goal is problem solving with math, then use the tools?
  • milobo says
    math needs to be a mix of fact based skills as well as understanding the how and why those skills are important.
  • milobo says
    yes, jackieb - it does come down to outcome!
  • mindelei
    just wants to say what a great conversation this is...this is the kind of stuff I have been waiting for!
  • budtheteacher
    mindelei - by "push back" I mean they asked me if that was really true, to think through it some more.
  • JackieB
    So, a student who has not "mastered" the basics can't have access to higher math?
  • mindelei thinks
    that purpose is very important. Kids need to see how these ideas relate to what is around them.
  • budtheteacher
    Push back meaning that there wasn't automatic agreements and head nodding.
  • JackieB
    And wouldn't use of available tools help in that?
  • budtheteacher
    Must math be a linear progression from the basic to the higher order?
  • mindelei asks
    if someone hasn't mastered those basic skills how can they appreciate/learn the higher skills?
  • JackieB
    Papert has been reinforcing a lot of what I already do. :-)
  • mindelei asks
    What is papert?
  • budtheteacher
    or can kids, when they see a need, explore the fundamentals after tackling, or attempting to tackle, a particular tough problem?
  • JackieB
    And extending my thinking. Yay!
  • milobo says
    it's funny to me (a math teacher by trade) that people argue against basic skills in math and not reading!
  • mindelei wishes
    milobo would further clarify...
  • budtheteacher
    milobo - I'll push back about basic skills in reading. Kids need to be immersed in language. That's all.
  • budtheteacher
    Okay - it's more complicated than that - but learning to read isn't a linear process.
  • JackieB
    milobo don't we teach kids to read by having them actually read lit? Do we wait until they're "fluent" before they read.
  • milobo says
    but if they don't have the skills to interpret and appreciate the language, can they truly grow fully in that appreciation?
  • budtheteacher
    milobo - It's a recursive process. It's why kids read Hamlet six or seven times in school.
  • JackieB
    Yes, but you teach the skills in context, right?
  • milobo says
    agrees and thinks that kids that are kept out of higher math and reading because of a preceived lack of skills are being disadvantaged.
  • budtheteacher
    Louise Rosenblatt would be someone else for folks to look up here - she's a theorist who talks a lot about Reader Response theory.
  • mindelei
    Thanks for the link - I'll be sure to check him out!
  • milobo says
    (and having this conversation while also watching "History of the World" on TV isn't easy!)
  • mindelei
    Rosenblattt sounds good too!
  • budtheteacher
    It's way more complex than 140 characters - but basically she and others argue that reading a text is a conversation between a writer's . .
  • milobo says
    RE recursive - YES! and that should be the beauty of math - it's a spiral curriculum, not a linear one.
  • budtheteacher
    brain and the reader's brain. What's learned is what the reader takes away and blends with prior experiences.
  • budtheteacher
    So different readers will have different readings of the same text.
  • mindelei says
    milobo Plus, there's the intimidation factor in Math & Reading.
  • budtheteacher
    I think you could make a similar argument for math problems.
  • mindelei feels
    that each person does come away with something different - particularly in relation to symbolism.
  • budtheteacher
    How interesting it would be to take a look at reader response theory and twitter or plurk - talk about different experiences.
  • mindelei asks
    JackieB So - did you get more than you were looking for? :-)
  • mindelei says
    That would be interesting!
  • mindelei is
    Impressed that there are now 72 responses to this plurk.
  • JackieB
    No, this is exactly what I'm looking for. Keep it coming! budtheteacher, thanks for the new addition to my reading list.
  • JackieB
    And regarding the intimidation factor, if we keep trying to "drill" the basics, isn't that more intimidating/frustrating than ...
  • mindelei says
    It goes back to dividing fractions. Rather than learning how to actually cut things into smaller pieces, we simply flipped and multiplied.
  • JackieB
    here, let's explore this problem.
  • JackieB
    So, if there are tools that help them explore this (in the context of a larger problem) why not use them?
  • mindelei
    I'm not really into "drilling." I do agree that we do to much of that - no real learning. But you do need to get basic understanding.
  • milobo says
    if you have to "drill" for understanding, then the students don't really understand and then it is frustrating for students.
  • mindelei
    But do they understand what the tools are doing? I've been in countless science labs where there is no real learning of why/how.
  • JackieB
    What is "basic understanding"? Estimation? Ability to use the skill in context? Ability to do 10 of the same problem? To extend the problem?
  • JackieB
    mindelei Then the teacher isn't asking the right questions.
  • mindelei
    Ability to apply the skill to a new problem.
  • mindelei
    Maybe not new...but different.
  • mindelei
    Ability to determine how to use what I already know on something I don't know.
  • mindelei
    Or at least move in that general direction.
  • mindelei
    I should have a general understanding to think my way through things that aren't completely familiar.
  • JackieB
    Can't we use larger problems to figure out smaller ones we need to figure out first? Gives us a real reason to learn the concept?
  • budtheteacher
    What about "an ability to see what it is you need to know that you don't know - and seek it out."
  • JackieB
    Thanks Bud, that's what I was *trying* to say.
  • mindelei thinks
    that's a better explanation of what I was trying to say.
  • mindelei asks
    Hey - how do you get italics?
  • JackieB
    One * on either side gives you italics, **two** on either side gives you bold.
  • mindelei thinks
    these little plurk tricks are very cool.
  • milobo says
    budtheteacher As long as students know enough to know what they don't know... ;-) and that's where some of my students struggled.
  • budtheteacher
    Okay - so we agree on what we want kids to be able to do. The argument comes when we try to figure out *just how much* context is needed.
  • JackieB
    We agreed? What do we want them to be able to do?
  • mindelei thinks
    she agrees. But also believes it comes down to problem solving skills.
  • JackieB
    Ah, so problem solving. Then why do they need to be able to do it by hand?
  • budtheteacher
    mindelei - That's a bit circular - we learn problem solving by learning problem solving skills.
  • budtheteacher
    Okay - how do we learn those skills?
  • budtheteacher
    *By actually engaging real problems with a skilled facilitator in our presence.*
  • mindelei feels
    that by knowing it by hand they will have a better understanding of what types of shortcuts work best and when to use them.
  • milobo says
    the best way to learn any skill is to apply it authentically.
  • mindelei feels
    This also helps to identify which tools are of most assistance when solving similar problems.
  • milobo wishes
    I could stay up and hear the rest of this conversation! I'll check in again tomorrow.
  • budtheteacher
    Solving real problems isn't a linear process.
  • mindelei says
    It's like only knowing how to use Word. If I have the skills to use multiple word processing programs, I won't have issues when Word isn't
  • mindelei says
    available.
  • mizminh
    mathematics is beautiful, engrossing & challenging - having a firm grasp of the basics promotes appreciation, engagement & creativity
  • JackieB
    mindelei So, if a student can't solve a multistep problem by hand, but can with tools, they shouldn't investigate further problems?
  • mindelei says
    she never said that.
  • mindelei says
    that understanding how to go about things by hand helps with the use of tools. Only knowing how to use the tools doesn't help the process.
  • JackieB
    mindelei Sorry if I misinterpreted. I'm just not following your thinking.
  • mindelei says
    No problemo. Clarification is always good!
  • JackieB
    Can't it work in reverse? Knowing how the tools work can help in understanding?
  • budtheteacher
    Wish I could stick around. Solve this one for me, y'all. I need some answers.
  • mindelei feels
    that it could - but what about the ones who don't really understand the tools - just know how to enter data?
  • mindelei thinks
    that many kids who have math disabilities go undiagnosed which is partially why tools seem to help so much more.
  • JackieB
    mizminh I agree with your statements about mathematics, but sometimes we focus so much on the basics that students never get to the beauty.
  • JackieB
    mindelei If they are just entering data w/o understanding then the teaching isn't facilitating the process correctly.
  • mindelei thinks
    that tools shouldn't be substituted for knowledge. They help the process, but don't take the place of the process.
  • JackieB
    I agree. A tool without understanding is useless. I'm just questioning what the process is. (symbolic manipulation or problem solving?)
  • mindelei
    I think you need to know multiple routes to come to a solution. Providing the knowledge of how to do it by hand creates an additional route
  • mindelei
    I also think that allows you to have a better idea of what other routes are most worthwhile.
  • JackieB
    Okay. I agree it is a route. However should that route be a gatekeeper to other routes?
  • budtheteacher
    What about for problems that we don't know how to solve? Should students engage in those? Makes "by hand" or "with tools" irrelevant.
  • mindelei feels
    that learning "by hand" helps in solving unfamiliar problems.
  • JackieB
    Why would we work on problems we already know how to solve. That's boring. Unless it is to find a better/different way - then it's fun.
  • mindelei has
    a goal to get to that - using knowledge to engage in solving unknown problems.
  • mindelei thinks
    finding better/different way is where tools come in handy.
  • colleenk thinks
    that basic skilss need to be taught alongside authentic problem solving rather than before. (first plurk)
  • colleenk says
    skills not skilss
  • colleenk thinks
    a certain amount of fluency can make it easier to focus on the problem solving task especially in middle school and above.
  • JackieB
    I agree that fluency is a goal. But should lack of fluency stop further mathematical work?
  • colleenk thinks
    how we teach math should be revised from the ground up. We don't teach math with any consideration of the way children (people) learn.
  • JackieB
    I agree. However I'm working on change with the students I have (h.s.) It's tough to change their (and their parents) idea of what math is.
  • colleenk thinks
    fluency should NOT get in the way. Fluency is not an indication of a students' ability to do higher level math and should not be a barrier.
  • colleenk shares
    that she is having the very same problem where she is.
  • JackieB
    Yay! I just had a conversation with a friend (different school) who said students can't get into alg. until they've mastered basics, so they
  • colleenk wishes
    Mindstorms was required reading for parents.
  • JackieB
    put them in a year long "basics" course. I asked if they were that much better after a year, she said no.
  • JackieB
    Heck, I wish it had been required reading in my math ed courses.
  • colleenk
    Are you trying to integrate higher level problem solving into you classes? Are people questioning your curriculum?
  • JackieB
    We use a "reform" curriculum (next year is our 4th year, so first year of offering all 4 years). Lots of solving using graphing calculator,
  • JackieB
    we're incorporating more Sketchpad. Everything is "taught" in context of a larger problem. Some staff still entrenched in old ways, some ...
  • JackieB
    parent confusion (though less now), still various levels of staff buy-in. I'm still questioning my own thinking (hard to undo they way I was
  • JackieB
    taught to think about what it means to "do math".
  • JackieB
    I'm also questioning what kids need to know to be "ready" for college. (I'm teaching the senior course - 1st time we're offering it).
  • mizminh
    the "by hand" usage is interesting. Mathematical skills are best developed by moving from the concrete to abstract -graspable to symbol
  • JackieB
    Hmm. What if the tool allows them to "grasp" the understanding. Isn't looking at a graph or a list or computer output more concrete than
  • JackieB
    symbolic manipuplation?
  • mizminh
    we speak of levels of abstraction maybe levels of concrete :-) or "graspability" would be useful
  • JackieB
    How would you quantify that? Wouldn't it vary from student to student?
  • mizminh
    of course & that is the eternal pedagogical challenge - differentiation- catering for the individual learner
  • mindelei asks
    What are the final goals? Different majors require much different math skills in college.
  • mindelei says
    Earlier it was mentioned that "by hand" wasn't necessary because most of this stuff wouldn't be used after HS anyway.
  • mindelei
    wonders which aspects can be made more relevant. The process of thinking through the problems is what can be taken beyond the classroom.
  • mindelei asks
    Which other aspects can be taken beyond the classroom?
  • JackieB
    I want them to take away problem solving skills, the ability to evaluate the solutions of others, to communicate solutions (and process) to
  • JackieB
    others, to have the willingness to tackle big/new problems, to be able to make a mistake and keep going,... just to name a few.
  • JackieB
    And that was part of my original question. What do students need to be successful in college? (not that that is my only goal, but ...
  • JackieB
    it is a factor - preparing them for future studies).
  • mindelei asks
    Is this one of those instances where it's more helpful to work backwards from your end-goals? Or at least look at that in conjunction with
  • mindelei asks
    initial goals?
  • mindelei likes
    the goals that you're working with so far.
  • JackieB
    Yes, but I'm trying to figure out exactly what the end goals are (I know mine, I don't know what colleges want. Want to make sure I'm taking
  • JackieB
    all things into account when I'm setting my goals).
  • mindelei has
    a suggestion: Check w/ some prof friends or local unis to see what they feel their freshmen are lacking.
  • mindelei
    That should be another good perspective.
  • mindelei
    I think that would be an excellent plurk - an alert to math profs.
  • mindelei
    I do have an opinion on what part of the problem is: not enough good math teachers at the elementary level.
  • mindelei
    I was an Elem Ed major, A LOT of the ed students had difficulties with the math courses we had to take (they only go through 8th grade math)
  • mindelei
    There are a few people I know who had to switch to Secondary Ed because they couldn't pass the math courses for Elem Ed.
  • mindelei
    Many had to take extra prep courses before math to get them ready.
  • JackieB
    And that is just indicative of the larger problem.
  • mindelei
    I think if we had more teachers who had a better grasp of math in elem and could better understand the problems the students are having
  • mindelei
    you would have fewer issues by the time those kids get to you.
  • mindelei
    Agrees on that point.
  • JackieB
    Yep, but blaming the el ed teachers isn't going to solve anything. We need to figure out how to teach the students we have now.
  • JackieB
    (and fix the system) :-)
  • mindelei
    Oh - I don't want to blame them...I just think they need to be better prepared too. It's a vicious cycle.
  • mizminh
    surely the goal is to have autonomous learners exploring their own meaningful learning environments.
  • JackieB
    Well, that's one of my goals. Will that help them in a college math class? With college admissions tests?
  • mindelei thinks
    mizminh has a way with bringing everything back to center.
  • mindelei says
    when you teach them well, the tests will take care of themselves.
  • JackieB
    Ah, but what if they can't use the tools on the tests? I'm still trying to figure this all out.
  • mindelei feels
    like we need a big white board or something. Do you ever watch NUMB3RS? I feel like we need to be making a big chart.
  • JackieB
    I thought this *was* the chart.
  • mindelei
    You could say that....but at the moment it has no sense of organization (although there is a definite flow). :-)
  • budtheteacher
    To be continued, right? Not finished?
  • JackieB
    Oh no, not finished by a long shot. Just my initial thoughts.
  • JackieB
    And I'd love for others to keep adding tot he conversation.
  • milobo thinks
    part of the problem when students get to HS is they see "doing math
  • milobo thinks
    "doing math" as adding/subtracting/mult/div whole numbers, fractions, and decimals.
  • milobo thinks
    and they "do math" with no connection to anything in the real world.
  • milobo thinks
    that's why they come to hate math in MS and HS. We need them to see that math is a form of language used to communicate and create.
  • milobo thinks
    the hand calculations are less important than the facility with understanding why and how you use each calculation to answer a question.
  • milobo loves
    that JackieB started this plurk and can't wait to see what others think!
  • mizminh
    what milobo said" math is a form of language used to communicate and create."
  • JackieB
    Thanks to everyone for their thoughts. I'm still processing what's here so far.
  • mindelei says
    I can't wait for the next conversation. That was a lot of fun for me and very interesting.

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