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Make Math Moments Academy Forums Mini-Course Reflections The Concept Holding Your Students Back Lesson 1 – Which Has More? – Discussion

  • Hayley Anderson

    June 11, 2020 at 1:39 am

    The difference between a direct and indirect comparison is the use of another object to help compare instead of placing the objects side-by-side or iterating. Direct comparison is “easier” when there are shared attributes (eg. the dots side-by-side).

  • Vanessa Cherney

    September 24, 2020 at 3:41 am

    Direct is putting the objects side by side and using spatial reasoning to compare them.

    Indirect is using another object, such as a piece of string, as the basis for comparing two objects.

  • Lauren Teather

    September 30, 2020 at 7:50 pm

    I like Hayley’s definition above – it made me realize that my husband does this all the time when we are out shopping for furniture or home items. When I’m considering whether or not something will fit in our home by eye-balling it (direct), he will use his hand to measure each object (how many of his hands wide is it?) to tell the difference in size between the objects (indirect) and also to compare it to how big the space in our home is.

    • Kyle Pearce

      October 3, 2020 at 4:38 pm

      Love it.
      Isn’t it interesting that many of the same “go to” strategies kids will resort to when investigating are still used by adults (like using our hands to measure).

  • Chris Laurie

    October 4, 2020 at 12:53 pm

    The number of simultaneous measures complicates our perception. Visually, we can easily draw a conclusion with a single linear measure. Secondly, comparing area requires experience to play and learn from different attempts and comparisons. Finally Volume, requires us to imagine (abstractly) even more. If students don’t regularly bake or manage liquid volumes how can they compare without experience?

    Developmentally, I know Kindergarten kids love their sandboxes and filling cups. Too often the toys and tools are left in the primary classes and too quickly substituted with paper and pencil in higher grades.

    When I am shopping, it drives me nuts trying to compare produces in various jars. Even when I read the volume label I have to fight my instinct not to grab the ‘taller’ jar. Marketers use so many games to mess with our perceptions.

    • Jeanette Cox

      October 16, 2020 at 1:29 pm

      I related to your example of grocery shopping. Yesterday I was looking for Arborio rice and found one container which through “direct” measuring looked bigger than the other container and was more expensive so I naturally thought it contained more but when I picked up the packages their net weight was the same. How my spatial reasoning fooled me. And your example of kindergarteners loving to play in the sand and fill containers reminded me of some research I recently did when writing the background information for geometry in K-2. Here is what quoted:

      It is important to note the importance of spatial reasoning. It is recognized beyond the limits of geometry, and the existing literature provides a firm basis for a conclusion that spatial ability and mathematics share cognitive processes beginning early in development (Cheng and Mix, 2014 p. 3; Davis et al. 2015; Jones and Tzekaki 2016; K-12, 2014, p. 3). Spatial reasoning seems to become crucial at the very beginning of math education.

  • Christina Michaels

    October 7, 2020 at 1:33 pm

    Direct comparison is visually comparing two quantities. Indirect comparison would be using an object to help you compare quantities.

    As I was watching the video and being asked to pause and make estimates, I was thinking how my experiences influence my thinking– I knew the circumference of the glass would be much greater than the height of the glass because I’ve done similar experiments in the past.

    What stands out to me is the lack of experiences that my students have (or rather, don’t have). So many things that I just take for granted that I did as a kid, i.e. counting coins from my dad’s change jar, or figuring out exactly how many tokens I could get for the arcade from how many dollars i had.

    As students’ realities change, so do their experiences. It just drives home the importance of me, as their teacher, being able to recognize what primary experiences lead to developing and understanding concepts, and then how to make sure my students have access those experiences.

    • Chris Laurie

      October 9, 2020 at 9:11 am

      Our class collected change for a Terry Fox fundraiser. I was surprise how little experience my grade 5 students had with counting coins. I searched through Jump Math for some worksheets to practice. There were no practice pages beyond the grade 3 level in Jump Math. For my weakest kids I gave them a hundreds chart to assist with counting change. Maybe I need to assign visiting a garage sale on the weekend?

  • Nicole Jackson

    October 15, 2020 at 5:20 pm

    With direct comparison, we use spatial reasoning skills to eye how one thing is relative to another thing. In the process, one of the “things” become the unit of measure.

    With indirect comparison, an additional object is utilized as the unit of measure by which all other things will be measured. And the idea is to judge how each thing relates to this unit, or additional object.

  • Christine McLaughlin

    October 21, 2020 at 10:22 pm

    The visual examples you share are such a good reminder for teachers. I wonder…how do teachers create these examples? I realize we can find some, but they are limited. And, how do we know if they are quality and will lead to the understandings we want students to gain?

    • Kyle Pearce

      October 23, 2020 at 6:40 am

      Creating is one way to go… there are many resources readily available though.

      If you are creating, my biggest recommendation is not to over commit time to the creating part – focus more on the planning and teaching part. Those are of utmost importance!

  • Krista-Lynne Edwards

    October 25, 2020 at 11:12 pm

    I really enjoyed the examples given in the video about comparing and I am working on building a few ideas into both my grade 8 and grade 9 courses.

    Indirect unmeasured comparison is the idea of using another object to help measure, such as referent points on a body.

    Direct unmeasured comparison is placing the objects side by side and comparing them visually. This is often easier when the objects are similar and we are being explicit with what is being compared.

  • Brent Sturtevant

    October 31, 2020 at 1:57 pm

    First off, great lesson. It gave me a lot of ideas of how to approach my lessons differently and, as mentioned before, that I need use visuals more often.

    Direct comparison is when using two of the same objects to figure out the answer (such as which one is bigger, etc) and indirect is using another object to help figure out the answer.

    As mentioned in previous posts, there is so much in real life situations that these discussions can occur and should be used in our lessons – shopping at supermarket.

    • Aaron Davis

      November 1, 2020 at 5:50 am

      Lets try this again (tried responding a few days ago and it all disappeared).

      As many have said above, direct comparison is where objects are compared side by side, visually compared (eye-balling it). An indirect comparison uses another object (like a string) to help make a measurement.

      Opportunities to provide experiences for children to make such comparisons like cooking and baking are great for developing their spatial reasoning.

  • Rajwant Cheema

    November 26, 2020 at 7:11 pm

    I see direct comparison as looking at the objects to compare which is sort of making prediction. Indirect comparison is when we use another object to compare the items which is almost similar to confirming predictions.

  • John Sasko

    November 30, 2020 at 9:20 am

    Indirect comparison involves the introduction of a third, “foreign” object that will be used to compare the other two. Direct comparison is when you make the comparison using only the two objects (like two arrangements of dots).

  • Robin Bergen

    April 5, 2021 at 10:39 am

    Robin Bergen

    Indirect comparison is when you use an object to tell the size. I use my thumb all the time because it is about an inch. Direct comparison is when you eyeball it.

  • Merrillee Reboullet

    October 17, 2021 at 11:13 am

    It seems to me that a direct unmeasured comparison would be a hands-on or physical manipulation of the objects or images to find the similarities and the differences, whereas an indirect unmeasured comparison would be more of an “eyeballing” approach, using prior references or understandings to apply our spatial reasoning skills.

    In this video I was reminded that students need to physically explore mathematical concepts, leaning into the direct unmeasured comparisons to really understand why the measured comparisons work. I do incorporate this into my instruction, but probably not as often as I should. Time always seems to be the issue, but then, what good is it to press forward when the understanding is minimal at best and not retained. A good reminder with a fun exploration. Thanks!

    • Kyle Pearce

      October 18, 2021 at 6:35 am

      It is always nice when we bump into a few reminders of ideas we have used in the past, but maybe not as routinely as we might like.

  • Kyle Ferreira van Leer

    October 18, 2021 at 8:07 pm

    Direct is putting them next to each other and comparing using spatial reasoning/visuals. Indirect comparison requires the use of an outside unit or tool to help measure more discretely (for example the blocks in the popcorn task).

    I love the idea of using these comparison tools to introduce circle work in middle school, to help students make conceptual connections before algorithms!

  • Lavon Heath

    October 30, 2021 at 1:02 pm

    Direct comparison is comparing using the object itself as the unit of comparison. Indirect comparison is using another object to measure it.

    As I watched the pizza example in the video, I realized how uncomfortable I am without a formula. I immediately wanted to crunch number rather than use spatial reasoning. I was taught math through formulas rather than through the development of number sense and that’s how I initially taught math. However, there were so many students I encountered who can’t memorize and for whom that old school approach was/is not effective so I am loving the idea of building number sense and problem-based learning. I do have students like me, however, who just want to put numbers together so I appreciate having great examples to use such as the ones you provide. I really think it will build better than understanding in the long run.

  • Tara Henderson

    November 4, 2021 at 4:04 pm

    Indirect reminds me a bit of “nonstandard” units, since kids use an object to estimate and measure height, width, volume, etc.

    I also relate to the grocery shopping – and the arborio rice is the most misleading! One package comes vacuum packed like a solid brick and the others are bags! You have to look at weight.

  • Kristin Snell

    November 4, 2021 at 10:18 pm

    The difference between direct and indirect comparison is the use of another object to link the comparison. I realize that I have encouraged my students to use what they already know about spatial reasoning to estimate something in an image. I just never really realized how much that helps them in proportional reasoning as well.

    • Kyle Pearce

      November 5, 2021 at 6:33 am

      These ideas are also new for us as well. It still fascinates us!

  • Kathleen Rushinsky

    November 12, 2021 at 7:47 pm

    The difference between a direct and indirect comparison is with indirect comparison you are using another object to help compare instead of placing the objects side-by-side (direct) or iterating.

  • Amy Johnson

    November 18, 2021 at 9:42 am

    Direct comparison is comparing using standard measurements or the actual objects side by side to compare.

    Indirect comparisons are using other objects in non standard ways to aid our spatial reasoning and compare how attributes or the measurements such as area or volume seem to compare.

    • Kyle Pearce

      November 19, 2021 at 6:33 am

      Great work reflecting and sharing your reflection here! With each post you are solidifying your own understanding!

  • Luke Albrecht

    January 7, 2022 at 12:17 pm

    I like the direct comparisons as students get to explore first and then leading them to formulas using unit comparisons (i liked the unifix cubes standing in for popcorn !).The big idea of “unit” comes up again. This has been so powerful in my thinking about teaching and learning.