tag:blogger.com,1999:blog-1907702537884089718.post7826987435130346495..comments2023-10-07T09:26:02.868-07:00Comments on Exit 10A: Down the Rounding Rabbit HoleJoe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-1907702537884089718.post-84302093974642169062017-09-16T11:00:51.298-07:002017-09-16T11:00:51.298-07:00Who knows if you'll see this or it's too l...Who knows if you'll see this or it's too long ago! First of all I don't even know you but love your name because for 38 of my years on this earth I was Natalie Schwartz. Now I'm married but anyway! <br /><br />I have been struggling with ROUNDING for the last few weeks as well as last year! I'm in Missouri and our standards say that students should use rounding as a means of estimating. Our curriculum (mostly engage) uses number lines which I really love because of the number sense but after reading your blog I'm starting to understand what you meant by a cognitive load. A few things have happened to me recently and I think I'll blog about it today. Trying to get better at that. Can I put the address for your blog in my blog and respond with my thoughts?Natalie Moon @themathgirlhttps://www.blogger.com/profile/10510196450864544608noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-30839753212588463622016-12-13T13:53:14.937-08:002016-12-13T13:53:14.937-08:00Thanks Mark!Thanks Mark!Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-6906268472634648792016-12-09T05:51:04.082-08:002016-12-09T05:51:04.082-08:00Joe I have added a link here for resource that Ont...Joe I have added a link here for resource that Ontario created a few years ago called the Effective Guides to Instruction. This one is the K-3 Number Sense. There many more on all areas and up to grade 6. There is some really good info in here on the number sense big ideas with instructional strategies and what students should know in each grade. It may not line up perfectly with you curriculum but you may find it useful.<br /> <br />http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_3_NSN.pdf<br />Anonymoushttps://www.blogger.com/profile/08283291764124745874noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-22916534116552948412016-12-09T05:47:39.965-08:002016-12-09T05:47:39.965-08:00We see this consistently with our expectations fro...We see this consistently with our expectations from our Ontario Curriculum, there is a lot more math going on underneath the expectations and many teachers are lacking content knowledge for unpacking and it affects their ability to set up learning opportunities for the kids. We are doing a PLC at one of my schools with that right now. Having the teachers look at the expectation and then find what are the key understandings that make up that expectation. A good example is one of our grade 3 fraction expectations. "Divide whole objects and sets of objects into equal parts, and identify the parts using fractional names without using numbers in standard fractional notation."<br />One example of key understanding that is required for students to truly understand this expectation is that the parts have to be equal area but not necessarily the same shape, they also don't have to be adjacent.<br />When we did our PLC not one of our teachers knew that about fractions. So unpacking these expectations is critical in my opinion. Obviously from Marilyn's comment and yours Joe that many of the Common Core Standards are similar. Love these conversations!Anonymoushttps://www.blogger.com/profile/08283291764124745874noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-43103732385010712002016-12-06T14:19:50.060-08:002016-12-06T14:19:50.060-08:00Thanks for your observations. It's fascinatin...Thanks for your observations. It's fascinating to hear how the concepts we deal with in elementary school play out for students further on in their mathematical educations. I'd be curious to know the kind of role rounding plays in university science classes. What kinds of rounding would they do? To what place value? Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-69393622533958018492016-12-06T14:11:14.204-08:002016-12-06T14:11:14.204-08:00Thanks Marilyn. I agree that teachers are doing t...Thanks Marilyn. I agree that teachers are doing their best to help students answer the kinds of questions that 4.NBT.A.3 generate. There's like a rounding cottage industry going on! To me it's indicative of something. Maybe something wrong with the standard itself? I think what's bothering me is its dissociation from any context. Estimating has an important purpose, and rounding helps us estimate. So rounding exists in service to estimating. Does rounding have a purpose on its own? Can lead a purposeful existence without estimation? Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-25722655679150164622016-12-06T13:52:50.011-08:002016-12-06T13:52:50.011-08:00Thanks Graham. It's another example of piling...Thanks Graham. It's another example of piling a concept on top of a shaky foundation. And I wonder if students who can round successfully really understand what they're doing. Maybe they're just better at memorizing and following the "rounding rules." Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-18939204498194260302016-12-06T13:50:27.003-08:002016-12-06T13:50:27.003-08:00Thanks Mark. I would agree that unitizing is over...Thanks Mark. I would agree that unitizing is overlooked. This comes into play in a big way when students are asked to round, say, 289,962 to the nearest thousand. I think your board is smart to invest time there, especially in primary classrooms. Place value scaffolds, like the place value flip book I used with the student in the post, don't get close to this concept. And neither do the arrow cards, although I like them because they help with expanded notation. In don't think I've ever really gotten a secure foothold on how to best teach it. It's a work in progress for sure.<br />Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-67630663129285447412016-12-06T10:18:10.957-08:002016-12-06T10:18:10.957-08:00I’ve been working with fifth graders recently on e...I’ve been working with fifth graders recently on estimating answers to multi-digit multiplication problems, and the issue of rounding has been on my mind. I remembered that I wrote a response to a teacher’s query about rounding and included it in About Teaching Mathematics. It addresses rounding and estimating together. (I've tweeted it -- can't figure out how to paste here.) <br /><br />First and foremost, I think both estimating and rounding have a purpose, and I work to keep the reason for doing either evident. About the standard: 4.NBT.A3, you’re right about an enormous amount being crammed into that seemingly simple statement. Many of the standards fall into this category―seeming simple but really embodying an incredible about of math. I think that many CC standards are packed this way, but I keep in mind that the standards aren’t and do not claim to be a curriculum, so deciding how to teach what’s needed for students to be successful with any standard is still up to curriculum developers, teachers, etc. <br /><br />There is so much wrong, in my view, with your curriculum materials and the sadly funny collection of best-intention charts and rhymes you included to point out the gimmicks and tricks teachers rely on. But teachers are trying their best to help students be able to answer the questions posed in the text you’re using. <br /><br />Marilyn Burnshttps://www.blogger.com/profile/16127025673987723020noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-71397935506225450422016-12-06T07:43:12.010-08:002016-12-06T07:43:12.010-08:00This idea that rounding follows place-value unders...This idea that rounding follows place-value understanding is very interesting, and rings true for me. I have to help university students in science classes who do not know how to round, and it is a very useful insight to relate it to their place-value understanding. It seems the students who have trouble with rounding often also have trouble with scientific notation, which is also a place-value thing.David K Butlerhttps://www.blogger.com/profile/02351781945972297201noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-21904445356173977282016-12-06T06:08:43.618-08:002016-12-06T06:08:43.618-08:00Great post Joe!
Thanks for tackling the rounding ...Great post Joe! <br />Thanks for tackling the rounding beast and sharing these strategies. It seems like were too quick to jump to "rounding" when many students don't have a foundational understanding of place value. Makes total sense why it's an issue.<br />Looks like this would be a great chapter for your book. That is... if you were to write one.Anonymoushttps://www.blogger.com/profile/08525114028095675402noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-18855788058422807972016-12-06T05:47:54.567-08:002016-12-06T05:47:54.567-08:00Hey Joe,
I like your strategy you used with this s...Hey Joe,<br />I like your strategy you used with this student. The expanded form really makes them look at the value in the place. I see this with teachers I work with all the time, teaching rounding as a an abstract concept by itself without any context. Putting numbers on the board and asking for rounding to specific place values. Like you said we really only round for estimating, so I think it is so important to teach it in contexts that make sense to them. I like the term creating friendly numbers which also ties into many operations mental computation strategies. The number lines are also excellent models for this, that's why I think your strategy using the expanded form will work so well. Makes it easier to see the friendly number. Honestly though how often to we get asked to round to specific place values? Not often. LOL. I think possibly another missing piece that often gets looked over in place value is the key understanding of unitizing. I often see teachers teaching the place names, that the digit value changes based on the place but unitizing as it applies to place value is left mostly to calendar time when students bundle groups of ten as they track school days or something in that vein. Our board has addressed this as being a need in our primary classrooms. We also see a gap in students understanding of zero as a placeholder, which is also a key understanding of place value. I wonder if some students lack of unitizing also affects the area you are speaking of in your blog? Thanks for sharing again! Always look forward to your blog posts!Anonymoushttps://www.blogger.com/profile/08283291764124745874noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-2470712603451861122016-12-06T02:00:32.567-08:002016-12-06T02:00:32.567-08:00Thanks John! There was always something about it t...Thanks John! There was always something about it that didn't seem quite right. So this begs the question: Is it the standard itself that's faulty, or does it have to do with the way the standard is interpreted by teachers and curriculum writers?Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-74540492064352258782016-12-05T16:57:05.412-08:002016-12-05T16:57:05.412-08:00It makes sense to me that you dislike rounding - I...It makes sense to me that you dislike rounding - I think it's purposeless preloading that we traditionally do so much of in math. It's not benchmarks, which are useful, it's not significant digits, it's not estimating. Do it b/c I told you to, with an arbitrary rule (5's round up) thrown in.<br /><br />You instead turn to place value sense making, which pays dividends for the rest of their life. Kudos, Joe!John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.com