High School Students Who Can't Multiply and Divide

Discussion in 'Secondary Education' started by Galois, Oct 6, 2012.

  1. Mathemagician

    Mathemagician Groupie

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    Oct 7, 2012

    Again, quickly filling in holes and stopping for curricular aims is different from turning the class into remedial math 101/BSI.
     
  2. czacza

    czacza Multitudinous

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    Oct 7, 2012



    I don't think anyone suggested that. Students come to us at varied levels. Pulling a small group, offering extra help, finding other resources in the school for them are all ways to make a difference for struggling students. The OP seems to be looking for such help for the students s/he teachers.
     
  3. LouiseB

    LouiseB Cohort

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    Oct 7, 2012

    I do have sped kids and in 7th grade they still add using their fingers. There is NO WAY I will ever have them up to 7th grade in just one year. I totally understand that they are sped kids and would never be in a school that required taking a math test to enroll. I do understand that schools can have that requirement because they are not public schools and can have that requirement. I do know of other 7th graders who do not know their math facts. It is not an unusual thing.
     
  4. McParadigm

    McParadigm Companion

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    Oct 7, 2012

    It's pretty much a repeating theme of skills-based classes like Math and English that teachers are frustrated every year by what their students don't know or can't do, and so then proceed to use the same basic designs that didn't manage to successfully teach the kids before to try and get it sorted out now.

    Obviously the way we're teaching isn't working, or the problem wouldn't exist in the first place. It's important to remember that the massive technological changes of the last 20 years (as late as 1994, there were still news segments being produced regarding what exactly this internet thing was) haven't just changed the way adolescents perceive, evaluate, and interact with the world...it literally changes the development of the brain.

    I remember my dad talking about how sometimes he and his brothers, at young ages, would watch news or educational programs when the weather was bad because there was nothing else on (if they weren't reading books, of course). Two channels will do that to you. By the time I was growing up there were more like 50 channels. Today, I literally watch the show I want to watch when I want to watch it. I send a note to my friend instantly, when I want to send it. I get the information I want the moment that I decide to seek it. Kids who play video games actively explore and impact entire worlds. Passivity just isn't much of a thing.

    This can bring with it a concern about attention span or refusal to learn, but these can be easily addressed by creating scenarios that involve horizontal relevance and active learning scenarios. In fact, I would argue those two things are NEEDED in order to make learning genuinely accessible. Traditional teaching approaches were built on a culturally prevalent background skill set...a set of assumptions that could be made about what children were capable of doing and what their home lives prepared them for. That set is rapidly being replaced. Continuing to hold on to traditional practices, and not seeking to create a new model based on the new skill sets available, is only going to lead to more surprise at how little next year's kids seem to know.
     
  5. Cerek

    Cerek Aficionado

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    Oct 7, 2012

    On the other handprints like practice, repetition and drilling DO still work. We learn through repeated experience. The more you practice a skill, the more automatic that skill becomes. Technology hasn't changed that, it's just given us different skills to learn.

    My boys could log onto the Internet by the time they were 4, but that's only because they had seen me do it and memorized the steps. They then took that knowledge and applied it to new items (laptop, iPod, etc) as they encountered them.

    Schools now teach "keyboarding" instead of typing (and offer the classes at a much younger age), but the exercises in the new books are no different than the ones in the typing books I learned from. The kids are still using the same skills, they are just using it on new technology, and they are still learning those skills the same way I and my parents did - through repetition and practice.
     
  6. McParadigm

    McParadigm Companion

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    Oct 7, 2012

    Unquestionably, practice can be a valuable approach. But that doesn't equate to saying "I showed you it, and we practiced it, so you should know it." Practice can be a valuable part of the natural way that the brain learns...as when your boys learned to access the internet or when a child is learning to play a sport....but only if horizontal relevance is present as well. There's very little evidence that practice minus motivation or interest accomplishes much.

    Computer usage in schools still leans so heavily in favor of teachers that students exhibit motivation responses toward any opportunity to be on the computer themselves. Basic keyboarding classes gain from this. However, one of my favorite lessons I had involved the kids responding to a book they'd read by creating a simple computer game based on it. They accessed and explored guides on how to use PowerPoint to make the game, they designed and constructed it themselves, and they made what were very impressive simple games based on the experiences and motivations of the characters in the book....at the same age that they were being given basic-level computing classes.

    Computing classes in schools tend to run well below what the students are capable of accomplishing.
     
  7. Cerek

    Cerek Aficionado

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    Oct 7, 2012

    I agree students are capable of much more than we often realize, but that isn't the case here. In this case, we are talking about kids who can't multiply or divide. Drilling them on multiplication tables WILL correct this. It may not be fun for them. It may not be exciting (although the teacher could find ways to remedy that), but it WILL be effective.

    Horizontal relevance is great in many situations, but math - by nature - has a great deal of vertical relevance as well. If students don't have the basics, they simply cannot move on to the more advanced skills, no matter how enticing or exciting the teacher makes the lesson.

    I often compare basic math skills to free throws in basketball. They may not be exciting, but most teams won't win the game if they don't make free throws..and the only way to become better at free throws is to practice. It isn't as exciting or dramatic as a slam dunk, but the average player will have many more opportunities to shoot free throws than to do slam dunks.

    Michael Jordan was SO good, he could literally hit a free throw shot with his eyes closed. How did he become that good? By shooting free throws over and over and over in practice. Not very glamorous, but very effective.
     
  8. McParadigm

    McParadigm Companion

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    Oct 7, 2012

    So we should probably assume that these students have never been exposed to multiplication and division in a drill-and-practice type classroom before? Does it really strike you as likely that the innumerable masses of students who reach high school with insufficient math or writing skills have simply never had teachers who made them practice?

    Horizontal relevance is essential for learning, and can come in a good many forms. Genuine curiosity produces horizontal relevance. Having success in a skill or concept tied to a larger goal you value can produce it, as well. Some students come by these things naturally, but most do not. Simply brushing it aside as nonessential, rather than strategizing a way to incorporate it, is sabotaging your own efforts.

    Nobody's arguing otherwise. However, simply providing students with a toolkit of functions doesn't produce thinkers. It produces believers in the toolkit. Teaching skill A in a way that incorporates exploration and active learning produces students who are going to be much more swift and capable of acquiring skills B and C, because they will be more aware of themselves as learners and have a greater sense of how to interpret and address the problems that may threaten to impede their own learning.

    Kids practice free throws because they want to make the team, and they want to be good basketball players...just like your kids WANTED to be able to access the internet. So it is exactly an example of horizontal relevance. They also make tiny adjustments to their efforts as they experience success and failure, as they actively pursue the correct form and "push." They'll take advice, they'll work with others, they'll practice and practice and practice...because they want it and are making decisions about how to achieve their goal.

    By loving it and wanting to.
     
  9. giraffe326

    giraffe326 Virtuoso

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    Oct 7, 2012

    I am the only teacher in my K-5 school doing multiplication drills (and I teach 5th :eek:). The 4th grade teachers used to do it, but 2/3 of them left a few years back. Now no one does it. So I have to find time to do it, because I only have about 4 (of 27) that know their facts.
    So, yes, assume away. It could very likely be true.
     
  10. Galois

    Galois Companion

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    Oct 7, 2012

    Thanks for all your excellent inputs. I'm learning a lot. Motivation is indeed the key. But, I'm glad that my 12-year-old son, who is now in 7th grade and who does not like math at all, was drilled by his teachers in his basic math starting in grade one coupled with doing accelerated math. He is now turning from a "C" to an "A" student as he approaches algebra.

    Still, the debate goes on as to whether to spend lots of hours teaching high school kids basic math skills. Just remember, we agree to disagree.
     
  11. McParadigm

    McParadigm Companion

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    Oct 7, 2012

    If we're going by personal observation, which doesn't seem like a very mathematical thing to do :)whistle:), drill has been by far the most prevalent approach at both of the schools I've worked at (which also featured plenty of vocal frustration about students not having "the basics"). If we're going to look at it a little bit bigger...

    If that last source strikes you as silly, that particular information is available in a lot of places...it just happens to be a rather succinct summarization, is all.

    --

    Having said all that...drill and practice fans tend to perceive it as a case of 'one or the other,' which is a huge fallacy. Practice opportunities are, as I mentioned before, essential. It's the format, function, context, and results they produce that decide whether they are impactful or not.

    Learning is a natural event. It is an inborn survival skill. The great summation of being. And the brain is an evolutionary learning powerhouse...physicist Sir Roger Penrose once called it the most perfectly organized part of the universe. 84% of the genes in your DNA are in some way associated with the brain. It isn't just good at learning...it was BUILT for it.

    But like all natural events, learning rests on a bedrock of catalyzing prerequisites. And this is exactly why this awesome learning machine seems to inexplicably meander through our schools with an exhausting indifference. Just as you cannot control fire without accepting the laws that define it and the characteristics that nature has imbued it with, you cannot maximize the potential for learning without doing the same for the brain.

    Disequilibrium doesn't occur because you say "You need to learn this," or because you say "This will be on the test." It occurs because someone is trying to achieve something that they want to achieve, because they have a personally set goal, because they want to understand something that they don't currently understand. It occurs because someone tells you "A newborn baby has 94 more bones in its body than you do." It occurs because you tried to build the tallest tower out of five sheets of paper, and your design failed. It occurs because a skill becomes relevant to either a real life or simulation experience that you are actively engaged in. There are a thousand ways to promote it. Why on earth would anybody want to shrug their shoulders and say "I don't think I'll do that?"
     
  12. Cerek

    Cerek Aficionado

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    Oct 7, 2012

    Nobody is saying we shouldn't try to produce deeper thinking and understanding of the concepts. I include critical thinking problems in almost every class assignment.

    If kids don't have the basic tools in their toolkit to begin with, though, then they simply are not properly equipped to attempt these types of problems. You can't build a house if you don't even know how to hold a hammer or saw, much less use them correctly.

    When the toolkit is empty, acquiring those tools (and learning how they work) does need to be the first priority.

    Not exactly. Many players do understand the importance of free throw and practice them on their own (like Jordan), but many more do not like free throws and never really try to improve them. Shaquille O'Neal is the perfect example. Yes, he loved the game and all the fame it brought, but he was a horrible free throw shooter. Every knew it, including Shaq, but he never put much effort into improving his free throws because that wasn't as glamorous as doing Monster Dunks. Shaq also refused to take sad vice from different people on his shot. Rick Barry (a former NBA player) told Shaq he could improve his free throw accuracy tremendously if he would start shooting them underhand (often called a "Granny Shot"). Rick shot his free throws like that when he was a pro player. He offered to work woth Shaq for free and guaranteed Shaq would improve his accuracy up to at least 85%. Shaq's response? Naw, man. I can't shoot like that because it doesn't look cool. So Shaq was more interested in "looking cool" than actually improving one of the most fundamental skills in the game.

    So the horizontal relevance still doesn't ensure kids will be totally motivated to learn the basic skills. You can explain the importance of the skill, you can show that doing the skill IS cool (like Jordan shooting with his eyes closed), but at the end of it all, the ONLY thing that will actually improve that skill is practice. Even if a player hates practicing free throws (like Shaq), they will still improve that skill if they are made to practice it over and over.

    I'm not shrugging off the importance of relevance to increase motivation and do my best to find real-world applications my students DO like, but when they don't have the most basic tools, I have to work on those first.
     
  13. McParadigm

    McParadigm Companion

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    Oct 7, 2012

    And you learn the tools BECAUSE you are building the house, or the deck, or the go cart...which is exactly the point. I learn how to use the Black and Decker screwdriver, and a million other "basics" like how to space my efforts and how to cut boards, and I get a LOT of practice at each...all within the context of an achieved goal. The toolkit is not divorced from the larger problem solving dillema. It is developed through active, authentic, and project based practice.

    Relevance is a matter of goal and perception. That said, the metaphor is imperfect because we're talking about creating opportunities for natural learning of specific skills within schools. Shaq was an adult rejecting one skill out of a large set. Its more akin to a student mastering some math skills but rejecting Calculus, while the situation in schools is like entire basketball teams not only failing to have the most basic skills, but not even fully understanding the rules of the game.
     
  14. McParadigm

    McParadigm Companion

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    Oct 7, 2012

    I'm really glad this thread popped up today, because I'm stuck at a child's birthday party and all the other parents are watching TV or texting. I was just gonna use the Nook app to finish reading a book, but this has been more fun. :)

    There's no better way to really clarify your thoughts, even within your own head, than in the context of debate, I think.
     
  15. ChristyF

    ChristyF Moderator

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    Oct 7, 2012

    This debate is raging in my school right now. 80 -90% of our kids coming to us not knowing their facts,. The 3rd grade teachers use rhymes to have them memorize their facts. They don't hold on to them. With the new common core there is more focus on teaching numeracy and true understanding of what the facts mean. I'm hoping this means kids come to us more prepared. We spend a lot of time teaching past skills.
     

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