How to correct visualization of mathematical expressions?

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This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say




2 + 3 = ?




and then the student usually replies with 5. Albeit they're not wrong, it's not the idea of commutative property. I feel that students so conditioned early on to see that 2 + 3 is necessarily 5 as opposed to understanding that 2 + 3 can just be that: 2 + 3. I had this problem myself growing up.



How can I address this issue?




2 + 3 = 3 + 2







primary-education arithmetic-operations







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  • In textbooks, typically at the high school or college level, one often sees instructions phrased as "Perform the indicated operation and simplify."
    – user52817
    1 hour ago







  • 1




    $2+3= sqrt5+sqrt3+sqrt30+sqrt3-10sqrt5+sqrt3$ or whatever other expression. It depends on the exercise, do you want them to calculate or to use the commutative property? Usually when someone ask me what is 24+87 I add them.
    – BPP
    59 mins ago











  • Is your question essentially "How do I elicit a response from a student that shows understanding of the commutative property of addition?"?
    – Joel Reyes Noche
    44 mins ago














up vote
1
down vote

favorite












This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say




2 + 3 = ?




and then the student usually replies with 5. Albeit they're not wrong, it's not the idea of commutative property. I feel that students so conditioned early on to see that 2 + 3 is necessarily 5 as opposed to understanding that 2 + 3 can just be that: 2 + 3. I had this problem myself growing up.



How can I address this issue?




2 + 3 = 3 + 2







primary-education arithmetic-operations







share|improve this question























  • In textbooks, typically at the high school or college level, one often sees instructions phrased as "Perform the indicated operation and simplify."
    – user52817
    1 hour ago







  • 1




    $2+3= sqrt5+sqrt3+sqrt30+sqrt3-10sqrt5+sqrt3$ or whatever other expression. It depends on the exercise, do you want them to calculate or to use the commutative property? Usually when someone ask me what is 24+87 I add them.
    – BPP
    59 mins ago











  • Is your question essentially "How do I elicit a response from a student that shows understanding of the commutative property of addition?"?
    – Joel Reyes Noche
    44 mins ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say




2 + 3 = ?




and then the student usually replies with 5. Albeit they're not wrong, it's not the idea of commutative property. I feel that students so conditioned early on to see that 2 + 3 is necessarily 5 as opposed to understanding that 2 + 3 can just be that: 2 + 3. I had this problem myself growing up.



How can I address this issue?




2 + 3 = 3 + 2







primary-education arithmetic-operations







share|improve this question















This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say




2 + 3 = ?




and then the student usually replies with 5. Albeit they're not wrong, it's not the idea of commutative property. I feel that students so conditioned early on to see that 2 + 3 is necessarily 5 as opposed to understanding that 2 + 3 can just be that: 2 + 3. I had this problem myself growing up.



How can I address this issue?




2 + 3 = 3 + 2







primary-education arithmetic-operations




primary-education arithmetic-operations






share|improve this question















share|improve this question













share|improve this question




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edited 21 mins ago









Tommi Brander

1,1391726




1,1391726










asked 1 hour ago









Lenny

1706




1706











  • In textbooks, typically at the high school or college level, one often sees instructions phrased as "Perform the indicated operation and simplify."
    – user52817
    1 hour ago







  • 1




    $2+3= sqrt5+sqrt3+sqrt30+sqrt3-10sqrt5+sqrt3$ or whatever other expression. It depends on the exercise, do you want them to calculate or to use the commutative property? Usually when someone ask me what is 24+87 I add them.
    – BPP
    59 mins ago











  • Is your question essentially "How do I elicit a response from a student that shows understanding of the commutative property of addition?"?
    – Joel Reyes Noche
    44 mins ago
















  • In textbooks, typically at the high school or college level, one often sees instructions phrased as "Perform the indicated operation and simplify."
    – user52817
    1 hour ago







  • 1




    $2+3= sqrt5+sqrt3+sqrt30+sqrt3-10sqrt5+sqrt3$ or whatever other expression. It depends on the exercise, do you want them to calculate or to use the commutative property? Usually when someone ask me what is 24+87 I add them.
    – BPP
    59 mins ago











  • Is your question essentially "How do I elicit a response from a student that shows understanding of the commutative property of addition?"?
    – Joel Reyes Noche
    44 mins ago















In textbooks, typically at the high school or college level, one often sees instructions phrased as "Perform the indicated operation and simplify."
– user52817
1 hour ago





In textbooks, typically at the high school or college level, one often sees instructions phrased as "Perform the indicated operation and simplify."
– user52817
1 hour ago





1




1




$2+3= sqrt5+sqrt3+sqrt30+sqrt3-10sqrt5+sqrt3$ or whatever other expression. It depends on the exercise, do you want them to calculate or to use the commutative property? Usually when someone ask me what is 24+87 I add them.
– BPP
59 mins ago





$2+3= sqrt5+sqrt3+sqrt30+sqrt3-10sqrt5+sqrt3$ or whatever other expression. It depends on the exercise, do you want them to calculate or to use the commutative property? Usually when someone ask me what is 24+87 I add them.
– BPP
59 mins ago













Is your question essentially "How do I elicit a response from a student that shows understanding of the commutative property of addition?"?
– Joel Reyes Noche
44 mins ago




Is your question essentially "How do I elicit a response from a student that shows understanding of the commutative property of addition?"?
– Joel Reyes Noche
44 mins ago










1 Answer
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2
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One way to see if the student understands the commutative property of addition is to have "fill-in-the-blank" questions such as
$$2+3=3+__$$
and
$$2+3=__+2$$
or even perhaps
$$2+__=3+__$$






share|improve this answer




















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    up vote
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    One way to see if the student understands the commutative property of addition is to have "fill-in-the-blank" questions such as
    $$2+3=3+__$$
    and
    $$2+3=__+2$$
    or even perhaps
    $$2+__=3+__$$






    share|improve this answer
























      up vote
      2
      down vote













      One way to see if the student understands the commutative property of addition is to have "fill-in-the-blank" questions such as
      $$2+3=3+__$$
      and
      $$2+3=__+2$$
      or even perhaps
      $$2+__=3+__$$






      share|improve this answer






















        up vote
        2
        down vote










        up vote
        2
        down vote









        One way to see if the student understands the commutative property of addition is to have "fill-in-the-blank" questions such as
        $$2+3=3+__$$
        and
        $$2+3=__+2$$
        or even perhaps
        $$2+__=3+__$$






        share|improve this answer












        One way to see if the student understands the commutative property of addition is to have "fill-in-the-blank" questions such as
        $$2+3=3+__$$
        and
        $$2+3=__+2$$
        or even perhaps
        $$2+__=3+__$$







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 37 mins ago









        Joel Reyes Noche

        4,73711549




        4,73711549



























             

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