Ch. 4: Practice Padlet by Ellen Burnett https://padlet.com/ellen_burnett1_1/93gywu7nc8m2 As part of our discussion and reflection of chapter four, please review the VDOE's Strand Introductions for Number & Number Sense for K-2, 3-5, and 6-8. Also, review the VDOE's five Process Goals for Mathematics. en-us 2019-04-12 15:10:04 UTC 2024-06-02 15:49:31 UTC hello@padlet.com Grades 3-5 Number & Number Sense ellen_burnett1_1 https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350961468 2019-04-11 20:17:17 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350961468 K-2 Number & Number Sense ellen_burnett1_1 https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350961705 2019-04-11 20:18:17 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350961705 Grades 6-8 Number & Number Sense ellen_burnett1_1 https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350961793 2019-04-11 20:18:40 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350961793 Click Here First! ellen_burnett1_1 https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350962124 Please read the Strand Introductions for Number & Number Sense for K-2, 3-5, and 6-8, as well as the VDOE definition of Computational Fluency (each taken from VDOE Curriculum Frameworks).  Click once on each item to enlarge it.  Then, add your own posting in the column you work with most, addressing these questions:

1. What do you think about facts vs. flexibility?
2. How can we help stakeholders understand the importance of teaching
 for true number sense?

Please review your colleagues' posts in other columns.

Please add any additional thoughts under the Computational Fluency column.

Bonus for regular Padlet users:  Please offer feedback on how to use Padlet in class and to make it more engaging in this column!]]> 2019-04-11 20:19:52 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350962124 Computational Fluency ellen_burnett1_1 https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350964200 2019-04-11 20:26:37 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/350964200 Toni Martin https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351499344 I think there is a place for facts AND flexibility...I don't think it IS a "vs" situation. With basic math facts like we cover, it's sometimes easier to GET the flexibility portion after they've got the facts down and vice versa. One of the first things we do at the beginning of the year is to teach them what an addition strategy is...often to students who already KNOW the answer to a basic math fact...2+2=4.  Going backwards from fact to flexibility is harder. However, when we get to adding 2-digit numbers, they are able to break place value columns down into basic math facts and see the patterns that emerge, so flexibility-first is the way we can go there. Many things that build on something else allows for more flexibility because they already know what the end result should be. I did like the idea of "low floor, high ceiling"...making sure EVERYone can do some part of what we're working on.

I think our part in a flexibility situation is in teaching students HOW to discuss, respond, and listen respectfully to one another. This is something that takes a lot of time, though...especially with "that" class who couldn't talk nice to each other if you paid them...and it often goes by the wayside because it is so time-consuming to stop and reiterate to them for weeks-on-end about how to discuss, respond, and listen respectfully. It's way easier just to teach the fact-based math than to allow the time flexibility requires.

]]> 2019-04-14 19:31:42 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351499344 Chris Martin https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351522344 There is absolutely a place for Facts in Math.  Students struggle with number sense because many of them don't have the necessary factual basis to learn more.  A huge problem that we run into in 6th grade is that most of the "Number Sense" is done without a calculator.  So, Math Facts must be known!  There is also room for flexibility, but I think facts must come first.  For example, we do changing fractions to decimals and percents.  If you don't have a calculator and you don't know basic math facts; how can you successfully perform this task?

I try to how important it is to have good number sense by doing my Math talk each day. However, if I knew how to make all students and parents understand how important it is to have good number sense; I would be a rich man! So to be completely honest; I'm not sure what the answer is. ]]> 2019-04-14 23:48:00 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351522344 Chris Martin https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351524267 I tell my kids daily that for most topics in mathematics, there isn't one single answer or one single method to solve and get that answer. Recently we have been covering balance point and mean. We did an activity where we went outside and used the sidewalk as a number line and practiced finding balance point. After we did this we talked about how this was a real life example of finding an average or a mean and the kids said, " I wish we could do all things this way!" My answer was that when we do the computation mathematically and pictorially that we are trying to be flexible and build their repertoire of  different strategies to solve problems.]]> 2019-04-15 00:07:45 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351524267 Krista Dunn https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351823708 I believe that it is hard to have facts vs. flexibility especially in Kindergarten.  They have to have the basics of math skills before getting to the flexibility part. In Kindergarten, they are just learning their numbers and beginning to decompose and  work with numbers.  I feel like the term flexibility would come later in their math education.  I can see in the grades beyond Kindergarten how you can have flexibility once you have the basic math fact knowledge.  

The second question is hard to answer.  I do number talks everyday  with my students.  Repetition in Kindergarten is key.  I explain to my students and parents the importance of understanding number sense through my weekly newsletter.  I give examples of what we are learning so the parents will practice at home with their child.  Some parents do not understand what number sense is and I feel like  I need to educate the parents just as much as the students.  ]]> 2019-04-15 22:30:17 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351823708 Krista Dunn https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351826467 I feel like it is my job as a Kindergarten teacher to lay the foundation for computational fluency. Computational fluency and number sense go hand in hand which recent research shows. I read an article that they are developed together and one can not exist without the other. I am interested in digging deeper into this idea and figuring out how it can relate to me as a Kindergarten teacher. ]]> 2019-04-15 22:54:16 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351826467 Response to Toni Martin by Alayna Allanson https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351834008 I totally agree that we need to get students to talk and respond to others regarding math. I think this is why number talks are so important, if you have the time, because it shows students how we all think differently about math and we can all be right even if we got to the answers in different ways. I think this would also help with students feeling confident in their mathematical computation.]]> 2019-04-15 23:57:13 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351834008 Alayna Allanson https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351834369 I think computational fluency such a hard and tricky skill, especially when we have SOLs that direct our teaching. We don't have as much time for all students to share how they got their answers and in turn, this puts the rest of the class at a disadvantage along with that students because there's no time for discussion. Sharing different ways to get an answer is a way to show students different strategies to use.]]> 2019-04-16 00:00:12 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/351834369 Chris, I totally agree with your thoughts! Facts have a place in our curriculum. https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352232829 2019-04-17 09:05:51 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352232829 Mrs. Whipple - In my opinion, I believe facts and flexibility go hand in hand. (Yes, old school here; 30 years) The mastery of facts seems to be the groundwork for opening the door to more conceptual thinking. That having been said, it is time to forge ahead into providing a great more deal of exposure to a variety of problems. On page 45, the bottom, a student says about an exam, "It's different, and the way it's there like - not the same . . . The story, the question; it's not the same as in the books, the way the teacher works it out." https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352234174
The author suggests teaching the facts more conceptually, using a variety of representations to represent the same fact.  That makes sense. 
Despite our access to technology, many teachers, even some new to the field, feel that it would be most helpful if instructors were given material that could easily be shared 
for the sole purpose of more conceptual practice in math. We search online ourselves for a variety of things , but iIt takes time. 

]]> 2019-04-17 09:16:01 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352234174 Ruth Kim https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352249833 I find it ironic that students who cling to formal procedures, as Boaler mentions, are typically the weaker students who do not know how to use numbers “flexibly”. As a result, they end up doing harder mathematics because they are unable to use their number sense to interact with numbers conceptually.  I do agree with everyone here on this forum that there is a place for facts in mathematics, but it needs to be woven in with flexibility. I’ve been trying more this year to let students discover the mathematics behind the standard procedures before just showing them how to do them. I have seen some students make those connections and the procedure now has a purpose and meaning rather than be a senseless procedure that they know just produces the correct answer. 

 

I think it’s difficult as teachers to get the students, their parents, administrators, and even themselves to really believe that number sense needs to be established before we ask them to constantly compute mathematical problems. Time is always an issue and as Janice mentioned, there aren’t many resources for teachers to use to try to change their teaching approach in regards to mathematics. Many of our student’s parents say that “this is not how I learned it” or “teach” their child how to do it in a more “efficient” way, not understanding that they are doing their child a disservice. 

]]> 2019-04-17 11:15:43 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352249833 Janice Whipple https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352398367 2019-04-17 18:41:38 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352398367 Ruth Kim https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352659814 Computational fluency I think is often mistakenly linked with route memorization and repeated practice. I myself have gotten frustrated with some of my lower students and preached the “practice makes perfect” line that I was told when I was a student. The book mentions that the famous quote “it takes roughly 10,000 hours of practice to achieve mastery in a field” is often misused in the education field to mean that in order to have computational fluency, we must keep having students practice these skills until the “just get it”. I wish I knew how to better approach students who may struggle with computation fluency so that they do not fall further behind or learn to be scared of or hate mathematics. 

]]> 2019-04-18 19:38:22 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352659814 Michelle McCall https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352957149 Mastering facts I feel is key and then we can build upon this basis with flexibility. Flexibility I believe ties in with the different strategies. Not ever student learns the same way. Some students can use number lines where other students can make a ten. Some students can  never get the concept of making ten. Why should we make them try to understand this? This is frustrating for them. If they can add on, count up, use a number line or a different strategy then they should be able to use whatever is best and easier for them. Math is about facts  and this is where we need to start. Math facts are the basic concept and without it they lose many concepts and understanding. 

]]> 2019-04-22 00:13:47 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352957149 Response to Chris Martin https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352957632 I agree with you that without the foundation of basic math facts then students cannot build upon further lessons. This begins in the lower levels. Students must learn basic addition, subtraction, multiplication, division, and fractions. Without these basic concepts, students cannot perform multi-step math problems or build upon the concepts such as double digit adding, subtracting and so on. 

]]> 2019-04-22 00:20:23 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/352957632 Alayna Allanson https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/353053904 Before I started reading chapter 4, I felt like for so many topics in math, especially multiplication, was simply remembering facts and had nothing to do with conceptual learning. After reading, the example for 17 x8 and they said to do 17 x 10 and then subtract 17 x 2 is something I had never thought about. It is so simple, yet it would get students thinking in another way. As several others mentioned, it seems like we are on such a time crunch for SOLS that we struggle to find time to fit in hands on things and time for deep conceptual thinking--we also struggle with the materials or ideas we need to teach our students in this way. 

As for those that don't understand the importance of true  number sense, I think it takes them to change their mindset and be open to seeing the difference. Giving them examples and resources could really help them to see how conceptual thinking in number sense is truly the basis of mathematical thinking in our topics.

]]> 2019-04-22 14:04:22 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/353053904 Kristin Acchione https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/353168685 I would like to think that facts and flexibility go hand in hand. However, I find the word “flexibility” a tricky one to link to math. I find that so often, especially with my kiddos that try so hard to grasp math concepts, they want to know how to do it, the process, or the steps. Some will make flashcards; others will repeat the steps or write them in the corners of their papers, flexibility or any deviation from these steps would make that much harder for them.  I try and show more than one strategy when I can and I will often use manipulatives so that students are able to see what’s happening. I think that creating instruction with the mindset of facts and flexibility in mind, would allow students to see that you can come to a correct answer by many different paths!

When thinking about number sense and its importance, I wonder if the best way to spread awareness is through resources and communication. I like the idea of math newsletters and parent resources. Let’s be honest, the way many of us learned math is not how we’re teaching it today. Understanding the new terminology (borrowing vs. regrouping for example) would be a small step in this direction. The other thing I’d like to see more of is vertical planning and research. As a 5th grade teacher, I often look at standards for 4th and 6th to ensure that I’m scaffolding and preparing my students properly. Perhaps if we did this a bit more we could identify areas of weakness and target it more directly.  

]]> 2019-04-22 19:51:24 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/353168685 https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/353604253 Jennifer Corrigan
I know for many years facts have dominated the thinking for learning math.  I do value the importance of knowing basic facts because it helps with processing speed and the ability to solve problems quicker.  With that being said, solving math problems quickly should not be the goal for teachers.  I do not value how quickly my students can recall their math facts.  I value their ability to use various strategies to solve math problems.  Their speed in solving the problems affects them more than it does me.  Processing speed influences a student’s confidence. The flexibility involved with understanding numbers and how they work together is as basic as learning “basic” facts.  Developing number sense seems more difficult to adults, since it is conceptual, but according to the research it is actually easier for children. So let’s encourage children to develop number sense, flexibility, as well the opportunity to learn basic facts if they choose to add them to their knowledge of numbers. I feel that both flexibility and facts are needed to be successful in all levels and types of math problems.

As educators it is our job to educate parents, colleagues, and society on the importance of teaching styles, strategies, and concepts.  This includes Number Sense.  Providing research results to support the validity of Number Sense will allow others to understand its importance.  Knowing that it could be easier for children to learn Number Sense as opposed to rules and procedures is vital.  Also, knowing that Number Sense leads to solving more complex math problems is another reason to provide the opportunity.   Understanding Number Sense can make learning math a more positive experience.  This might allow students to have an open mind to exploring math.  Bowler describes a mathematical mindset, instead of a fixed mindset for math, which allows students to compress math concepts so they can organize them and easily file them away for the future.

]]> 2019-04-24 03:22:45 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/353604253 Emily McNulty https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/354847847 Flexibility is an important component for having number sense.  Number talks can go a long way in helping establish flexibility with numbers giving students daily opportunities manipulating numbers and allows them to get used to sharing their ideas.  Most students who have flexibility with numbers also do well with their facts.  
I believe there are some students who have their facts down, but lack the flexibility because math to them is rote memorization and steps/procedures. Though, the knowledge of one's facts can also help students when they are learning multiple strategies to aid in flexibility.
The majority of my students (TI Math) lack ability in both fact knowledge and flexibility due to their poor number sense.  I find students can have mastery of facts without number sense, but they never have flexibility without number sense.
I think most stakeholders understand the importance of number sense, but may not feel as though they know the best teaching methods or feel constrained by time. I believe time can prevent teachers from focusing on things like number talks because they are in a rush to get everything in during the course of a school year. ]]> 2019-04-29 00:57:34 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/354847847 Using Both Sides of the Brain & Number Talks https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/355963116 "....the highest-level performers were those who exhibited the strongest connections between the two sides of the brain. " "....formal abstract mathematics that makes up a lot of the school curriculum is enhanced when students are using visual and intuitive mathematical thinking." (page 39) "Number talks are the best pedagogical method I know for developing number sense and helping students see the flexible and conceptual nature of math." (page 50) ]]> 2019-05-01 19:57:30 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/355963116 Chris Van Savage https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/356992223 I believe that both facts and flexibility are necessary in learning.
Not all students can easily memorize, though knowing facts through memorization aids when building in higher math.  Number Sense and reviewing with problem solving and more exploration of number sense may help all students to not fear understanding when it comes to facts. I see in 7th grade that some students fear multiplication facts because they feel that they don't know them and now can't learn them. We proved with squares and square roots that everyone now knows larger numbers (to 20 squared) and can easily see smaller facts. I remember the timed facts tests and the anxiety if caused for me!]]> 2019-05-05 22:17:43 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/356992223 Chris Van Savage https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/356993510 Computational fluency needs to include strategic thinking and flexibility, not just memorization. I think in math for so many years math facts meant flash cards and timed tests. Students that didn't master the facts the first time around were left behind as learning moved on. We as teachers can help with math anxiety with facts by engagement and strategic teaching, not just memorization. Making sure we catch late learners of math facts and engage them to achieve success will prompt positive feelings about math. I do find that having SOL's does take away from having additional time to create this type of daily learning environment in our classrooms.]]> 2019-05-05 22:31:23 UTC https://padlet.com/ellen_burnett1_1/93gywu7nc8m2/wish/356993510