So, welcome everyone.
As you are entering the webinar, please feel free to type your name and the organization in the chat box,
so we know who you are. So this is a webinar using the Teaching Fractions Toolkit to support evidence-based instruction in sixth grade. We'll start in a minute. All right. I see people are still signing in. One more minute and then we'll get started. All right, let's get started. So welcome again, everyone. This is a webinar using the Teaching Fractions Toolkit To suppo
rt evidence-based instruction in sixth grade. Next slide, please, Melinda. So the webinar is hosted by the Teaching Fractions Toolkit Partnership
at the Regional Educational Lab Midwest, REL Midwest. My name is Yinmei Wan, and I'm the Partnership Director and also the principal investigator for the Teaching Infractions Toolkit evaluation study. With me today is my colleague, Melinda Griffin, who is the partnership manager. Melinda is a Math Education Expert,
and she's also a former classroom tea
cher. Next slide. Before we start, I do want to note that
we will be recording today's webinar, and the recording will be archived
on the REL Midwest website. We will be sending out an email Letting you know when the recording is available. So this is the American Institutes for Research, which is the organization that manages REL Midwest, and this is our standard recording notice. Next slide. So here's a brief agenda for today.
I will start with a brief introduction of who we are and why we are
here today. Melinda then will take over to highlight some effective strategies
for teaching fractions on which the Teaching Fractions Toolkit is built. She will then elaborate on how
the Teaching Fractions Toolkit is designed to help teachers enact evidence-based strategies,
followed by a preview of the tool kit. We will then share some information
about an opportunity for districts and schools to gain early access to the Teaching Fractions Toolkit by participating in a study to help us evaluat
e the toolkit. We will close with a Q&A session. So you will have an opportunity to unmute yourself once during the webinar,
and also at the end of the webinar, to ask questions directly to the presenters. But during the webinar, please also feel free to answer your question in the chat box, and we have people who are monitoring the chat box. We will be answering your question as the webinar is going on Next slide. So today's webinar is hosted by REL Midwest. REL Midwest is part of a network of
10 regional education labs funded by the Institute of Education Sciences, the research arm of the US Department of Education. REL Midwest works with educators in Illinois, Indiana, Iowa, Michigan, Minnesota, Ohio and Wisconsin, to support the use of evidence and data
to improve student outcomes. In particular, we seek to address priorities related to the needs and outcomes of students who are furthest from opportunity. Next slide. So the webinar features the Teaching Fractions Toolkit, which inc
ludes a suite of new
professional development resources and supports designed to help teachers learn and implement evidence-based strategies in fractions instruction. In the last 2.5 years, REL Midwest has worked collaboratively
with educators from a field of schools and districts, to develop, test, and refine the toolkit. During the 24/25 school year, we will be conducting a study to further evaluate the efficacy of the toolkit,
professional development and resources Through participating in th
e study, Grade six math teachers will receive
free professional development on evidence-based instructions, and teachers also will receive other classroom resources to support their implementation of those strategies,
such as like free interactive apps, assessment probes, and student tasks. School and district leaders will receive resources that will help them support teachers. This is also an opportunity for districts to build capacity for future professional development. Districts will have th
e opportunity to send their local staff to be trained as co-facilitators, so that they can going forward facilitate PD themselves. So we will share a little bit more information later in the webinar about how to become involved in the study. But before that, I’d like to turn it over to Melinda, who will share more about practical strategies
that are featured in the Toolkit. Melinda also will provide a preview of the Toolkit. Melinda? Thanks, Yinmei. Good afternoon, everyone. I'm going to be teac
hing about fractions. I have to admit, I love fractions, as a former math teacher. We're going to be starting off by thinking about what strategies are effective for teaching fractions. I think a good question to lead that off is, why fractions?
Why are we worried about fractions? So we know that US students math skills have fallen short compared to our
international counterparts for many years, and the pandemic has exaggerated that as well. So fractions are often a topic in math
that shows gre
at underperformance, and often leads to difficulties as students make a transition to the middle grades. When they go to middle school, the focus shifts from fractions to ratios and proportions, but is building upon the fraction knowledge
that students develop in elementary school. What I'm telling you now is not new. You all know that students need to master fractions to make that successful transition. You've likely experienced this in your own classroom in working with students. As a teacher,
teaching fractions is sometimes frustrating. Oftentimes students have difficulty understanding that fractions are numbers too, and that much of what they've learned
in working with whole numbers can actually be transferred to fractions, but they've got to come to see fractions
as numbers in and of themselves. We also know that teachers benefit greatly from having additional strategies to teach fractions, and to build student understanding of how to work with them. We know that visualization is
an important tool when learning fractions. And so part of our goal with this toolkit is to give you some tools around that, to help your students understand fractions better. So the work that we're going to look at today is from a What Works Clearinghouse practice guide. If you're not familiar with these, What Works Clearinghouse presents recommendations for educators to help address challenges in their classroom.
This is based on reviews of research, opinions of experts,
and the experiences of
practitioners like yourselves. So this toolkit supports the practice guide Developing Effective Fractions Instruction for kindergarten through eighth grade, As you see here. There are five recommendations that are talked about
in this practice guide. The first one is build on students’ informal understanding of sharing and proportionality to develop initial fraction concepts. So this is what we often see early on with students in school, even prior to third grade, which is where the second recom
mendation often comes in, helping students recognize that fractions are numbers
and that they expand the number system beyond whole numbers. So this is where students begin to more formally
understand and use fractions. The third recommendation is to help students understand why procedures for computations with fractions make sense. We all know, and could probably remember, things that we learned very procedurally in math, that then make it difficult to work with later on. So our goal is to have
kids understand the “why” behind the operations that we do with fractions. We also have a recommendation that we should develop students’ conceptual understanding for strategies for solving ratio rate and proportion problems, before exposing them to cross multiplication as a procedure to use to solve such problems. So once again, having an understanding of what's going on, particularly in contextual types of scenarios is really helpful for students, as opposed to just,
here's the trick I do to
solve this. And the fifth recommendation from the practice guide
deals with teachers, and it says professional development programs should place a high priority on improving teachers’ understandings of fractions and how to teach them. The way fractions are presented to students now, and the way we help students get at fractions more conceptually, may very well not be the way we learned fractions ourselves. I know it's very different from what I saw when I was a child. So the more that we can wor
k with teachers and help them have a chance to learn and grow and understand fractions themselves, the better off this will be in the classroom with their students. I'm going to focus on two recommendations
from the practice guide today, and these are the recommendations
that a lot of our toolkit is focused on. So the first one is Recommendation 3, help students understand why procedures for computations with fractions makes sense. Here's a practical strategy that goes along with this. Tape diag
rams are helpful when
considering the whole versus part relationship that's often found in contextual problems. So Recommendation 3 talks about visually representing fraction operations through the use of area models, number lines, and other visual representations, to improve conceptual understanding of
more formal computational procedures. When we use a visualization, this allows students to estimate or judge
the reasonableness of their answers. So in our toolkit, we delve into how teachers can
use these visualizations to address some common misconceptions that come up in the classroom. We know that using real world context with
plausible numbers is helpful to students, because as they make a connection of the context with the math itself, students will have a greater chance of retaining knowledge of what that computation means. So you see here a problem where students are thinking about - this is a common problem you would see. There's five glasses of orange juice.
If a serving size
is 3/5 of a glass, how many servings of orange juice do we have? So you see the tape diagram here. Drawn out, we see the five whole glasses of orange juice shown, and then students begin to draw a separate fraction bar underneath to think about, if I have servings,
how many servings will be in that whole by showing both quantities together, students can start to make sense of the problem. We might have some students that catch on right away and kind of see what the pattern is. You might have som
e students that need to draw it out all the way to the end to get to their answer, but they then can take the drawing,
and relate what they have visualized for this to what that looks like in terms of fractions and the operation that happened to get there. I think this is particularly important for
misconceptions that often come up with students around fractions. Students often learn hints in the earlier grades, particularly when they're doing whole number computations. So things like when you m
ultiply two numbers, The product is always bigger.
Or when you divide, you get a smaller number. But these don't hold up when you move on to fractions. And so providing a visualization for students along with the operation itself,
helps them see what's actually going on in the problem. Moving on to Recommendation 4, develop students conceptual understanding of strategies for solving ratio rate and proportion problems before exposing them to cross multiplication
as a procedure to use to solve suc
h problems. So we have a practical strategy here,
that when solving rate problems, you can consider using a double number line to help visualize time versus distance. I like this one in particular,
because I think double number lines are something that often are not as familiar to teachers, but they make great sense when it comes to solving problems such as this. So when students enter the middle grades, knowledge of fractions is forming that foundation for it. So the more we can do to help them
see conceptually what's going on, the better. We explore the use of number lines
and area models quite a bit in our toolkit to help kids understand the conceptual background behind operations. The last part of this Recommendation 2 suggests providing opportunities for students to use and discuss alternative strategies for solving ratio rate and proportion problems. So what we see here is one example of a double number line, where the student has miles on the top, and they're comparing miles to
the number of hours
it takes to go those miles. We often see problems like this,
Like you need to go from here to there , and you're going to ride your bike or you're going to take a car,
and it takes this long. So this helps the students see both quantities. One child might put miles on top,
another child might put miles on the bottom. You have different ways of visualizing it, but both of them help with the comparison of those two quantities. This also aligns with mathematical practice standar
ds in which we ask students to persevere in problem solving, asking students to justify their own reasoning, and also to critique the reasoning of others. So when students use visualizations to solve problems, this gives them another tool to be able to talk with others
about what they have done through discussions with others,
they can help build their own understanding, And think about what makes sense and what doesn't make sense. I think this is also a great estimation tool for students, too.
And the understanding that they are going to get conceptually from working with visualizations S really critical to moving into work further on
in math beyond middle school. For example, when we get to functions in high school algebra, and also exploring similar figures in trigonometric ratios in high school geometry. So similar to the strategy of using a tape diagram, a double number line is useful in solving rate problems,
as we see here. In this example, we see them comparing things directly.
We could use this same approach. Maybe we have two riders that are both
trying to get to the same destination. Who is going to get there first? All we would need to do is add another number under there for the other writer, And we can still use that to compare the quantities across the board. All right. Let's move on and think about some additional evidence-based strategies that we're going to see in the toolkit itself. So the toolkit components were codeveloped, tested, and revised based on ba
sed on educator feedback. We had a great group of teachers from Illinois who've been working with us on the toolkit up to this point. There's teacher supports in here that are specifically focused for grade six teachers. Our thought being grade six is where we make that transition from fractions to ratios, rates, and proportions, so that's a good place to do some
solidification of fraction understanding. There's also leader supports included in here as well, which addresses fraction strategies a
cross grade levels, since administrators focus on more than one grade level within the toolkit,
there are six professional development modules. And if you look at these,
you see kind of the building of fraction understanding. We start with Module 1,
which talks about fractions on a number line. From there, we move on to understanding fraction
addition and subtraction. And our third module is understanding fraction
multiplication and division. In module four, we get kind of a mixture of those, an
implementation of fraction computation overall. And modules five and six focus on understanding
rate, ratio, and proportion, and implementing those in problem-solving. Each of the modules that you find in the toolkit include the same things. So each module has an exploration of math tasks included. There's some student work analysis. There's lesson planning and implementation guidance. There's the use of online interactive apps. And we also include a teacher reflection tool and formative assess
ments that can be
used with students as well. One of my favorite parts of the module
are the exploration of math tasks. They are tasks that you could use with
your student in the classroom, But the teachers themselves get to
actually experience the tasks, talk through them, and work through them with other people
as part of the professional development, I think that's hugely helpful for teachers. They get to see what's going on. They get to build their own confidence with
working with those frac
tions. I know from teachers we've worked with so far, they found that part hugely beneficial. Each of the modules follows a similar structure as well. The module spans about two weeks, and there are two facilitated meetings that happen synchronously. And then there's some other activities to be
completed between the meetings. So for example, you'll see for module one,
fractions on a number line, this has a focus on Recommendation 2, emphasizing number lines. there's an initial meeting that happe
ns where you
come together and do some work. There'll be some interim activities that people people complete individually,
and then you come back together again for a second meeting as part of that module. We also have supports for leaders as well, because we know for professional development, we need by administrators as much
as possible to make sure things continue to be a focus at a school. So leaders will find informational videos
and handouts that they can use to help them understand the t
raining
that their teachers are going through. There's also a monitoring conditions checklist. This is not meant to be an evaluation. It's meant to be a chance for the
administrator to go into classrooms, see what's happening, and see where they can further
support teachers in their learning. And there's also professional development facilitation materials with each of these modules as well. Oftentimes an administrator wears more than one hat. They may be the people that need to actually present
the materials with their teachers. It's also there in case there's a school-based math coach,
or perhaps a lead teacher, or someone who wants to pick this up
and work with a group at the school. All right. So let's take a peek at the toolkit itself. So within the professional development modules,
there's several components, we have a detailed facilitator guide. There are two slide decks that are already developed for leading those meetings with teachers. There are participant workbooks that tea
chers will have to do the work and thinking as they go through the process, and then the teacher reflection tool as well. So this is an example of a facilitator guide that we have. And within it,
you see an agenda and resources for leading this meeting. This is a kickoff meeting with teachers for module one. If you look to the other side, you'll see kind of a walkthrough of,
here's what's happening, but also some guidance on the right-hand side
around things that might come up during the meeting
that they need to address with teachers. Hints for moving the thinking forward where they need to. And sometimes just some background information
on why this is happening now. So this is hugely helpful.
As someone who facilitates a lot of things, having a guide to what you need to do
is always much appreciated. We also have participant workbooks
for each of the teachers. So a teacher will have within the workbook, the handouts. This might be something they use later with their students as well,
but they have a dedicated place to do the work themselves. Often there's room to actually solve or do the task, and then some questions for reflection that go along with it. You also see interim activities, they're on the right. There are some things that we're asking teachers to do in the meantime, between the first meeting and the second meeting
in this module. And there's a way there for them to actually be able
to click through and track what they have done. There's also links to be able to
get to different activities that they need to access. There are also slide decks for the meetings. You see some examples of these here. Nice, bright, and bold visuals of the different examples that you’re
putting in front of teachers. It can be very helpful to be able to put this up
in front of a whole group. Or perhaps if you have people joining virtually, they can pull it up on their own screen To be able to see the things that they're looking at. And there's formative assessment handouts. T
eachers work through this themselves, but these are tools they can use
in the classroom with their students. This one here is about locating fractions on a number line, and you'll see there's a multiple choice selection there on the left, So students have a place to do the work.
This can help teachers really get at, are students understanding the concept, and if not, what is the misconception that's happening. And so you'll see these activities build in terms of cognitive difficulty, which helps
you see perhaps where a
student is starting to veer off the path, which makes it much, much easier to do some intervention with them and help them get back on track. There's also some interactive apps that are found within this.
I'm going to switch my screen here for a minute and actually show you what these look like. These are still in beta testing, I will say, so they're not ready for public consumption quite yet, but we thought we'd give you a sneak preview anyway.
So let me stop sharing he
re. I will switch over to the screen that we need to see, and show you what these look like. All right. So our first one is locating fractions on a number line. Let me move some things around here,
so I can see what's going on as well. So in this case, students can put some fractions on the number line. They have a chance to move them around,
like maybe I put this here, and then I go wait, no, I think maybe it belongs over here. I can check the locations and see which ones I have right,
and whi
ch ones I don’t. I can then uncheck it and keep working if I need to. Maybe I move this one here, and I want to check again. Hmm. It looks like I still have some things going on. I can get a hint if I need to. And there's multiple problems in here as well, too, that I can look at with different fractions. The next one is comparing rational numbers. So this one is interesting,
in that I can start off with the bare fractions, I guess you would say, the naked numbers. And maybe I say, OK, I'm going
to compare
1/2 to 1/3. I might have a student who says, “I think 1/3 is greater because 3 is bigger than 2.” This is something that often comes up when students start working with unit fractions. So maybe I do the answer, and I go, hmm, Wow, one half is bigger. I wonder why? I can come down here
and I can also look at an area model of this, and this can make it much more apparent
why 1/2 is bigger than the 1/3. I might also want to look at it on a number line
and think about it that way. So it'
s a nice way to bring all of the
different visualizations As well as the more abstract fractions
that we're used to seeing in a classroom all together in one space
for students to be able to look at and compare. Now let's say we we've looked at those unit fractions, but maybe I want to look at some other fractions.
So I can drag this - and I go up to a whole –
but maybe I want to look at 2/9. And then what do we pick over here? We can do the same.
Maybe I want to look at different denominators a
gain, 2/5. Now, maybe instead of looking at an answer right away, let's look at the area model of it. When I do this Once again, if I still have a student who's thinking
that bottom number is bigger and that means everything is bigger, And they can now see that 9th is actually referring to a whole
that's divided up into nine different parts. And fifths, the same thing,
a hole but divided into five parts. So in this case, I can see 2/5 is bigger. I can also drag this bar back and forth if I need
to, to be able to talk about different parts of this. And once again, I can look at it on a number line. This can be helpful, in that if I have students who are thinking about benchmark fractions, I can pull up this number line. We can think about, here's our 1/2 spot. How do these two numbers relate to 1/2?
Both of them are less than 1/2, but how much less than 1/2? There's directions on here as well,
in case you need directions. And I know within our tool kit development as well, using the ap
ps is part of the professional development, and there's some really great screenshots and instructions that go along with these to help you use them on your own,
and then in your classroom as well. All right, let me come back to our PowerPoint, and we will keep on moving here. All right. I’m make sure I’ve got the right one. I do not.
Let me stop here and go back to the actual PowerPoint this time. All right. Bear with me for technical difficulties. Are there any questions we want to take
while
I'm messing with this on the side? I just want to say, Melinda, and jump in,
I think the PowerPoint sharing correctly for us. How you have it just now, the screen looks fine. OK. I know it's hard to see from the back end
what all is showing. I was not seeing it at all on my end, but that's OK. I'll share with what you all need to see instead. So let me come back to that again, I’ll share my screen. All right.
My only problem is I cannot move the slides forward how. Say it again, Yinmei? You can
click on the slide and see whether it advances. Yeah, just a second here. All right. Let's try this one more time. Anyone who knows me knows that I am the Bermuda Triangle of technology, and so this should not be shocking if things aren't working. All right. Let me come back to the actual presentation itself, and we'll try this again. Or if someone else from our team wants to share at this point,
you're welcome to. Yeah, I can answer.
Is our question about a time commitment for the program? I ca
n answer that one.
As Melinda mentioned, there are six PD modules. So with the exception of module one, for each module, it's one hour for the first meeting and one hour for the second meeting. And then within the interim activities, we expect it will probably take teachers two hours. So module one,
the first meeting will probably be longer with two hours, then meeting two will be one hour. So in total, it's 13 hours of meeting time, synchronous meetings,
or depending on your district, the prefe
rence could be in-person meeting. So it's 30 hours meeting time,
plus 12 hours of like interim activities, for the PD. All right. Does this look good, Yinmei? Yes. Yes. So what, fifth or sixth time was the charm here? All right. On this screen, you see some testimonials from
teachers that we've worked with in Illinois during the usability study. I'll let you take a read of those for just a minute. I would say they had a really positive experience with this. We always learn a lot from the educato
rs
we work with as well. So we also enjoyed the process, too. Melinda, we are seeing the normal view. It's not to like the presentation view, the slide view. I'm going to stop sharing then. Emily or Belema - I can share my screen, Melinda, I have it. That sounds good, Mia,
because we're going to switch over to Yinmei as well. And we do have some time for questions here,
if anyone has questions so far. If not, we can do some at the end, too. Is that showing up right for everyone? Perfect. Just le
t me know whenever you're ready for us to go ahead. Yeah, Melinda, we do have some questions. There is a question, is there a different way to to teach and not use cross multiplication? I have seen many mistakes,
because students have been taught their cross multiplication - I think Will Johnston will provide some good discussions here, But I wonder if you have any additional thoughts on that as well? I will say that Ted always has great wisdom around fractions, because like we work together som
etimes too. Thinking about as kids make that transition from fractions to proportions, I would always do what I called word fractions with my students, which would be setting up the actual quantities. But to the side, like, what are the two things
we're comparing in words? And then let's think about how much we have of this one,
And how much we have of that one? It would help them think about where is the unknown in the whole situation themselves? So I think that can be beneficial before you jus
t go to trying to write the proportion itself. It kind of gives a little bit of a scaffold
to think through it on their own. I'm trying to look at the chat now. Tad, what else did you have in there that was good? Yes, so finding the factor needed for equivalents. That says it much more eloquently than I did. All right. There was a question, why not just make 1s by multiplying both sides
by 15 in your first example? So that a question. All right. Should we go ahead and keep moving, Yinmei? Yes, w
e can. All right. Mia, we can go to the next slide. So, as I mentioned in the beginning of the webinar,
we will be conducting a study in the 2024/2025 school year to evaluate the efficacy of the toolkit. So findings from this study will be used to help us further improve the toolkit. So the toolkit resources will be available
to the general public after the study and after everything is finalized. But by participating in the study, schools and districts will have an opportunity to gain early acc
ess to the toolkit,
and start to use it now to improve teacher instruction and student learning. So we expect to be working with about 40 schools for the study. We are inviting public schools that serve students in grade six to join us. 20 of the schools will receive the toolkit PD and resources in the 2024/2025 school year, and the other 20 schools will will receive the tool kit PD and supports
in the 2025/2026 school year. We will kind of decide who will get the PD first or second through a lo
ttery process. Next slide, please. So again, I just want to reiterate some of the potential benefits for teachers here. So teachers in participating districts, they will receive training on the tool kit. And the training will be facilitated by REL Midwest staff virtually
or by a locally trained facilitator. That's another option. Teachers also will receive resources to use in their classrooms
to improve student outcomes, including the student tasks, assessment probes, and the interactive apps as
well that Melinda just showed us. Teachers do need to participate in data collection with us, so we want to be transparent about that. So the data collection piece includes
a pre and post-survey. Teachers will be observed by our staff for once in the spring, and then teacher will help us administer
a short assessment to students. It's about 20 fraction problems. Then some of the teachers will be selected for a virtual interview. So for those activities, teachers will receive compensation for up
to $150 for helping us completing that data collection. Next slide. So for schools and districts, some potential benefits include - so they will receive resources to facilitate their professional development, including the detailed facilitation guide that Melinda just showed us. And then there will be leader resources to support teachers in helping them implement practice guide or recommendations. And then schools and districts can receive summaries of research findings
specific to their school
or their district. So for the sake of time today, we don't get into the details of the study in this webinar. But we can answer any questions you have
about the toolkit and the study. Next. I do want to mention that we would also love to set up individual meetings with school districts who are interested in being part of the study, so that we can go over the details and discuss how participation would look like for your district or your school. So if you are from a SEA or another organization,
and you think a district in your state
might benefit from this opportunity, please have them reach out to us as well. We will provide information on how to reach us
at the end of the webinar. So for now, I mean, Mia, can participants unmute to ask questions directly? I think they should be able to do a raised hand function, And then we can unmute them if they would like to ask that way. Or they could enter a question in the chat for us as well. OK. For now, maybe we can pull the next slide up, w
hich is how to contact us. You can scan the QR code on the screen here. To contact Jennifer, who is our recruitment lead. You can also visit our website,
or watch a short video about the toolkit. I think that's it for the webinar. If you don't have questions for us,
feel free to log off. But if you have questions,
feel free to stay on and ask us as well. We will stay on the line to answer any questions. Thank you all for joining us, too. I appreciate it. You have a question:
As a participant in
the study are the modules part of the process? Yes. You'll work through all six of the modules that are
found in the toolkit as a teacher, and there'll be parts of them
that you can use with your students as well. One thing, you know, Yinmei, that didn't come up
that I think is always good to point out, this is not a curriculum to be use with your kids. These are tools and strategies for you to use as a teacher in teaching fractions. So you would continue your same
regular math curriculum that y
ou have. But this would just give you some more insights and things to use to make things go better with it. Yeah, just use any of the channels on the screen to contact us, and we can schedule a meeting directly with you or your district leaders to discuss this. I think we can wrap up. There are no other questions. Thank you everybody for joining us. Thank you. Take care. Bye-bye.
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