- [Presenter] Okay, today we are going
to talk about self-efficacy.
This is the final meeting in our training series
on building positive math attitudes.
And this session, if you look at the materials I sent you,
is a little lighter than what we have in the other sessions.
We don't have any specific teachers' guides
for specific activities.
And that's because the research on self-efficacy
really points to more broad classroom-based practices
in general that promote self-efficacy, which don't
lend themselves to nice, neat, tidy teachers' guides.
So in your materials for the self-efficacy session,
you have, per usual, a PowerPoint slide deck,
and then a facilitator guide to walk you through that deck.
I should say I'm joined today by Lauren Bates.
Lauren, do you wanna say hi?
- [Lauren] Hello.
- [Presenter] And we will start off by,
as we have in past sessions, about talking
about the research behind self-efficacy
before launching into those classroom practices.
This is a session, where I would start with an icebreaker
to get people thinking about their own self-efficacy.
And one way to do that is a question like this that asks,
think of a time when your performance surprised you,
a time when you succeeded or even failed unexpectedly,
and how did that success or failure impact your feelings
about yourself and your abilities?
And this is a nice question to get people really grounded
and thinking about what self-efficacy is,
because it is so tied to our actual performance
and our past experiences around performance.
We're gonna skip that question today,
but this would be a nice one to break the ice
and get people thinking about self-efficacy.
Our goals today are not only to define self-efficacy
and understand the roots of how it's formed,
but also understand the importance
of self-efficacy for outcomes for students,
including engagement, but also performance.
Particularly, of course, as we have
in our previous sessions, we're tying this directly
to students' experience in the math classroom.
So we'll end with some actionable strategies
for building students in math their self-efficacy.
This slide looks familiar to you, hopefully.
And this is Camille Farrington and her colleagues' model
of the kinds of things that promote
more positive academic outcomes.
And if you remember from our previous sessions,
and her very large review of what promotes
academic outcomes in the non-cognitive sphere,
she has a model where she suggest that the research
really points to academic mindsets
promoting academic outcomes by way of leading to the kinds
of academic behaviors we know are important for success.
And she has distilled that research,
She and her colleagues have distilled that research
into four key academic mindsets.
Today we're gonna be talking about the second of those
which is I can succeed at this.
And this is self-efficacy.
Self-efficacy is this belief tied to a specific task,
and it's what a person believes about their chances
of success at a specific task.
If we wanna get really jargon-y we can use Bandura,
the original definition is the belief
that one is capable to organize and execute
the course of action required to produce given attainment.
Really rolls off the tongue.
But we can nicely boil that down
into the belief about success at a given task.
Research on self-efficacy comes
from Dr. Bandura's research on social cognitive theory,
which was work pioneered by Bandura to try and understand
how people learn and the social aspects of that.
In today's session, we will talk specifically
about students' self-efficacy in the context of math.
It's really important when we think
about what self-efficacy is,
to remember that this is our perceptions
of our performance capabilities, specifically.
And that's in contrast to the kinds of belief we have
about ourselves more generally and about more kind of
global personal beliefs about our personal qualities.
So when we talk about math self-efficacy,
we're not talking about statements like,
"I am a math person."
But instead we're really drilling down to be more specific
and it's I believe, for instance,
I'll be able to solve this set of fraction problems.
It's really about performance and really about belief
in being able to execute and perform.
Another thing to keep in mind
about self-efficacy is it's very personal.
So we're talking about our judgment of our own capabilities
as opposed to how well we stack up against our peers.
We like this quote from Henry Ford.
"Whether you think you can,
or think you can't, you're right."
And we like this because it really nicely sums up
in a tidy little package, why as educators,
we should care about self-efficacy.
What we believe about ourselves and how we expect to perform
are really powerful influences on how we actually perform.
And this is because how we expect to perform
affects a range of other variables like motivation
and effort and how we respond to challenges in a moment.
Self-efficacy is tied to specific domains or abilities.
So this means a student might have different levels
of self-efficacy beliefs depending on the subject.
For instance, you might feel very efficacious
when it comes to English and writing
and your musical abilities, but have less of a sense
of self-efficacy in other domains.
You can drill down even further than that
and think about how students may feel efficacious
in some aspects within a domain but not others.
For instance, in a math classroom it's entirely possible
that a student could feel positive and efficacious
about certain types of math problems and not others.
Thinking about self-efficacy brings
to mind other forms of self-belief.
And I think it's important to take a moment and compare
how those different variables compare to one another.
So here we have a table we've adapted
from some resources from Transforming Education.
And I really like this for helping set the stage
for how self-efficacy is distinct from the concept
of self-esteem and growth mindset.
So self-esteem, this is students' more general
and global sense of self-worth.
Questions about who am I, what is my worth.
An example of a statement you might expect
from someone who has a high sense of self-esteem is,
"I am a competent person and a good learner."
So that kind of example shows and paints the picture
of really more broad beliefs
about the self and the self concept.
In contrast, self-efficacy, as we've been talking about,
refers to a person's belief that they can
actually carry out what's necessary
to achieve a specific task or goal.
So this is asking the question,
"Can I do this specific task?
"Can I do this specific set of problems?"
And then the answer, for instance, would be,
"Yes, I am confident I can solve these factoring problems."
Drilling down to the specific as opposed to the global.
And of course, growth mindset, which we've talked about
in previous sessions, this refers to a person's abilities,
a person's beliefs about whether their abilities
can change over time as a result
of effort, perseverance, and practice.
So this gets at beliefs about ability to grow.
Can I do this? Well, I can't do it yet.
But I know I can get better if I study hard,
try to start strategies, and seek help.
High self-esteem and a positive growth mindset are often,
or we would expect them to support
self-efficacy but they're different concepts.
It's easy to see and expect how these things
might be interrelated, though.
For instance, students with high self-esteem
that have generally positive opinions of themselves
are likely to start out in novel situations
with a strong sense of self-efficacy.
There is massive literature on the relationship
between self-efficacy and academic outcomes,
which we've summarized here with hitting some
of the key points about the kinds
of things self-efficacy is related to.
And I think this paints a really compelling picture
that teachers really should care
about their students' self-efficacy,
because we see that students with high self-efficacy
are more interested in their academic pursuits,
they persist longer, they're more engaged.
They also respond more productively and adaptively
when they encounter challenges or setbacks.
And of course they show stronger academic performance.
We also know that students are more likely to seek out
situations in which they are confident about their abilities
and they're more likely to avoid those
in which they are not confident.
So we've boiled down the research here but I think
what we're seeing is a story of where self-efficacy
is really an important driver of motivation,
which in turn impacts achievement.
Why would we expect students to try and put forth effort
if they don't believe they're going to be successful?
For a student who thinks trying is useless,
that they have no chance of succeeding,
it makes sense that they would disengage and be unmotivated.
Bandura's research in theorizing on self-efficacy
has show that self-efficacy beliefs are formed
by several overlapping factors that influence
an individual's self-efficacy beliefs in a given area.
And some of these are more potent
and more influential on efficacy than others.
Specifically, the four sources of self-efficacy
are first, mastery experiences.
This refers to a student's past experience,
whether or not they've had positive or negative experiences
with this particular activity in the past
or very similar experiences.
And these are gonna be the most influential
source of self-efficacy.
If a student had success last week on algebra, they are
gonna expect to be successful again in the current week.
The other three sources are less potent
and less influential but have also been shown
in the research to be connected to self-efficacy beliefs.
These include vicarious experiences,
when students have seen others who are similar to themselves
experience success or failure with an activity.
It's important to keep in mind here that students
are likely to discount a model that is deemed irrelevant.
So for instance it's much more powerful
to watch a peer succeed than it is to watch
a teacher model something successfully.
The other two components that influence self-efficacy
are social persuasion, people telling me I can
or can't do an activity, and finally,
physical and emotional states, whether or not
students have experienced a positive or negative
physical and emotional sensation
when they've engaged in an activity.
This probably reminds you of our talk about math anxiety
and how that physical sensation of nervousness
and anxiety is really connected to students' confidence.
So this is a quote from Bandura that nicely sums up
what we've been talking about,
"People's level of motivation, their affective states,
"and their actions are based more on what they believe
"often than what is objectively the case."
And so an intriguing way we display this quote
along with some key questions to start a discussion.
And let these questions get at
whether or not teachers agree that beliefs
are powerful determinants of academic behavior.
And also whether they see certain groups of students
who seem to enter the classroom with more or less
positive beliefs about their competence and ability.
And the purpose of this discussion is
to set up the next part of the slides,
when we return to this concept about how some students
are likely to step into the math classroom
with less positive attitudes than others.
And in our trainings we've often talked
about how gender can impact math attitudes.
You've seen this quote before about how
boys don't pursue math at a higher rate
because they are better, but rather it's because,
at least partially, they are better--
they think they're better, excuse me.
This slide should also look familiar,
where we have talked about how students' beliefs
about themselves as learners and stereotypes
that affect those beliefs are likely to play a role
in inequities we see in math and other science,
technology, and engineering fields.
I'm not gonna go through the specifics of this slide,
since you've seen it three times in the past now.
But this is a key point we wanna hit
in all of these trainings that helps people understand
why some students are more likely than others to come
into the classroom with a less positive attitude about math.
Now at this point we wanna transition
and get to the good stuff and talk
about classroom strategies to build self-efficacy.
So I'm gonna turn over the reigns to Lauren,
who's gonna walk us through this portion of the training.
- [Lauren] Hello, everyone, I'm Lauren Bates.
If you didn't miss, or if you missed
the introduction that Karen gave.
Thank you so much for joining us.
And as Karen mentioned, there's a little repetition
between what you've seen before
and what we're presenting today just because
these concepts overlap quite a bit.
But we're fully expecting you
to take ownership of these fly decks
and materials and tweak them as you see fit.
Or the teachers you're working with.
And so please feel free to, you know, take these modules
and cut and swap and do whatever makes sense for you
to be successful working with the teachers you support.
So when it comes to a classroom strategy,
we're gonna, I'll make sure that the studies
are typed up so they are aligned
to those four key aspects of self-efficacy
that Karen touched on earlier,
that are based on Bandura's research.
One thing that I'd like to point out for you,
is that we really went into, during the math anxiety session
we went into great detail on that physical
and emotional state point, that you need to attend
to the physical and emotional states
that your students are experiencing.
And so we're not gonna touch on that today.
But we will spend time talking about increasing
the likelihood that students feel success
building towards mastery, that we are cultivating
successful vicarious experiences for students,
and that we're providing positive
verbal persuasion or feedback to them.
So let's start with building mastery experiences,
which Karen mentioned is the most potent and powerful piece
of these four aspects of self-efficacy.
It's the one that seems to be the most influential.
And so for the strategy of increasing the likelihood
of success building mastery, there's a couple
different approaches that are pretty typical.
So the first of which is using scaffolding
to promote success, tasks that are appropriately challenging
for the students of the teachers you're working with.
The other approach is to help students
set goals and track their progress
so they can see the growth that they're making over time.
So it's likely that your teachers are gonna be familiar
with some key concepts from developmental psychology,
like the Zone of Proximal Development.
I just wanted to touch on that,
just so you can tie it in with them.
Vygotsky came up with this idea of
the Zone of Proximal Development way back in the 1930s.
I don't know if people realize that actually
what he's talking about is something
that can be described as scaffolding.
So when it comes to the Zone of Proximal Development,
the idea is that students have a space of skills
and knowledge in which they can work unassisted.
And that is that inner purple circle in this diagram here.
It's really sort of where they already have mastery.
But if we want students to learn and grow, we want to push
them into the sort of next level of difficulty,
which is that Zone of Proximal Development
in which a student can learn and can achieve,
but they need some assistance, some scaffolding,
from their teacher, from their peers,
from a carefully designed lesson plan, etc.
And then finally there is an outer zone
of things that are just too challenging for a student
to master at this given time in their development
and their growth, but of course over time
they will get there, it's just a matter of
occurrence of a particular time point for these students.
The idea of scaffolding is that the tasks
that a teacher is assigning should have students
in that Zone of Proximal Development,
so that there is scaffolding in place for them,
and that the teachers gradually remove the scaffolds
as the students learn the content or the task at hand
and have them gradually working up to mastery.
And your teachers are probably going to be very familiar
with this terminology, but it's just a way
to sort of frame this, or maybe a new way to frame this
as these things that are not just good teaching practices,
they also build self-efficacy for the students.
So scaffolding of course is a building term.
So one way to think of scaffolding,
is as a way of building support and building that support
into lessons that help students eventually get to
where they can independently do tasks that would initially
be too challenging for them without some support.
There's two different flavors of scaffolding
that are often deployed.
And those are bridges and ladders.
And in either case, the idea is that a teacher
thoughtfully in their lesson planning,
tries to develop incremental steps
over which a student progresses as they go
from easier to more challenging tasks.
And they gradually increase what they're able to accomplish.
A teacher also deploys scaffolding
when they're delivering instructions,
so there scaffolding appears not just in planning
but also in the delivery phase.
So let's talk about that bridge idea of scaffolding.
So this is thought of as a horizontal method.
It seems to me to be a strategy that would be most useful
in the moment when a teacher is actually delivering
instruction and needs to adjust on the fly
and deploy some scaffolding pretty much immediately.
And that is because to build a bridge,
a teacher is evaluating whether or not
what they're asking students to do
is actually allowing students to succeed.
So for instance, they would model an exercise
for the students with the intention that the students
could go work independently or work in small groups
and have some success, even with the scaffolds
of like structured worksheets to work on.
However, if the teacher is looking at the classroom
and sees that the students are not succeeding,
well then it's time to build a bridge.
They need to create additional practice tasks,
perhaps start a classroom discussion, so that the students
can have a little more support and get
a little more gradually slated direction from the teacher.
So in this form of scaffolding, you're not necessarily
increasing difficulty yet, but you're allowing more practice
and maybe giving some additional entry points
to the skills and knowledge that the students need,
so that they can succeed where they are.
So the next form of scaffolding is building a ladder.
And this is a more vertical method.
And this to me makes sense to think of starting
with the teacher's planning phase where teachers
work backward from what it is they want a student
to know and be able to do by the end of a lesson.
So what are those end of lesson expectations?
And working from that endpoint, building progressive steps
that build incrementally, that will allow students
to get up to that most challenging endpoint.
And that most challenging endpoint
can be thought of as the top rung of the ladder.
So as a teacher is lesson planning,
they can evaluate whether or not the examples
and exercises that they've built in are sufficient to help
get students all the way to the top of the ladder.
And if not, if there are some gaps,
then it's time to add some rungs
so the students have a little smaller
increment between steps up that ladder.
And so for this scaffolding, the difficulty is definitely
getting more challenging for the students
as they progress through the ladder.
So scaffolding is kind of a broad term.
There's lots of different forms
of scaffolding that can be used.
And so it's really important for teachers to know
different ways of scaffolding and to consider how
they can tailor the scaffolds they're gonna offer
to suit a range of learners that are in their classroom.
And some examples of scaffolds that are pretty universal
and can be used in math and other content areas,
are teaching academic vocabulary, which is vocabulary
that appears across content areas in the classroom,
but that's very important and meaningful vocabulary
for students to understand to be successful.
So an example of an upper elementary vocabulary word is
analyze, an academic vocabulary word
specifically, is analyze.
The students can hear that word in science,
they could hear it in math, they could hear it
in English language arts, they could hear it
in social studies, and so it's a term
that they need to understand well enough
to use flexibly across the curriculum.
And you don't want students to have to be thinking about
and mulling over those words at any point.
You want them to be comfortable with them.
So teaching academic vocabulary actually
is supportive of their math learning in the long run.
Another scaffold is to allow students
to use multiple modalities to learn,
which means that they're using different means of working
on a skill or grappling with content.
So they could be writing about it, they could be listening
to a lecture or video, they could be speaking about it,
for math they could be using manipulatives
to make it visible and concrete on some sort of operation,
they could be drawing a diagram of something for geometry.
And the idea here is that students use
different parts of their brains when they're engaging
in these different modalities and so they get
more depth of thinking about the content
when they're doing more things related to that content.
This is not the same as having
a different quote-unquote learning style,
for which there is very little research base.
This is more about depth of thinking and depth of cognition,
which is a really important distinction.
Another great strategy for scaffolding is making sure
you have different ways of making concrete
the sometimes abstract concepts in math
that students might struggle with.
I'm using a visual example.
And this can include not just manipulatives
that are right there in front of the kids and they can touch
but also videos and animations that you could find online
that show processes in action.
A lot of people will use the Khan Academy
for this sort of thing, although those videos
and animations are often kind of dry.
There's something that is great
about using things like videos and animations
to show examples, is that you can pause them.
And the kids can pause them; you can rewind.
So it gives them a chance to really--
if they're not getting the concept the first time,
they can take a little bit of control, have some agency,
and rewind and get some more exposure to the idea.
Finally, another scaffold that teachers can do,
is to model their actual thought process.
And this is something that students can be taught to do,
which we'll talk about a little more in a moment,
and that is thinking out loud,
so that the black box of what's going on
in a teacher's mind, is made explicit to the students.
And a teacher can, as they're, let's say,
solving an equation on the board, can be saying,
"Hmm, I remember here that this symbol is an addition sign
"and that means I need to take these two quantities here
"or these two digits and add them together."
And so that gives the students an insight
into what the teacher's strategies are,
what details are pertinent to the teacher,
how to interpret information that they're seeing.
That really just allows the students
just a different entry point into actually
what's going on in the teacher's brain,
which can be very powerful for students who are struggling.
And these scaffolds are good for any sort of student,
but they're especially helpful for English learners,
if you have those in your school in great numbers.
So another interesting way of using scaffolding
is to use what are called low floor, high ceiling tasks.
And we found some great examples of these at youcubed.org,
which is a website by Stanford and Jo Boaler,
so knowing how much work Jo Boaler has done
in Washington State you might already be familiar with this.
But if you're not, I highly recommend you go
to youcubed.org and you can look at their task library
and that is completely filterable.
You can select specifically low floor, high ceiling tasks
and then grade levels for those things to be filtered.
And the idea of low floor is that it's something
that has an easy access, even beginners can have
some success trying this task.
But high ceiling is that it's challenging enough
that even more advanced students will be challenged.
So it's kind of an interesting sweet spot for tasks,
where students from a variety of different levels
can get an entry point and allows them some success.
So the game I've put up here is called Circles and Stars
and that's just one example of,
I think it's for the third grade level,
low floor high ceiling tasks that you can see
that if a student who is maybe just barely learning
to think about multiplication could start working on
through that concept in a more basic visual way,
but then a student that has been learning
more multiplication can be actually doing the multiplication
in their head and just getting more advanced practice.
So something that you might want to discuss with teachers
while you're addressing this idea of scaffolding,
is just asking them to think about if there's a tension
between supporting student's mastery experiences
and also making sure there's enough challenge for students.
Some ways I've heard teachers talk about this
is the difference between boredom
versus productive struggle versus frustration,
and really trying to have students
in that productive struggle space.
Sometimes teachers like students to feel
like they're having mastery, but if you stick
only in areas where students have mastery,
you're in that innermost circle when we look
at that diagram of the Zone of Proximal Development.
And so they may not be getting enough challenge.
So this might be fertile territory for you to discuss
with your teachers, to see what they think on this.
And maybe that could give you some insight
on how to work with them to make sure
that their students are getting enough challenge.
Alright, so the other strategy
for building students' ability to reach mastery
and building their success there,
is to help students set goals and track progress.
And just like the scaffolds, there is this idea
that you need to set a large goal, your larger goal
for the lesson or for the unit
or whatever thing you're working on,
and you need to break it into smaller chunks
that are foreword progression,
you know, developmental sequence
going up to the most challenging task.
And you wanna set small, attainable goals along the way.
So the goals are meant to challenge students
but still be achievable and it gives the students a chance
to track their progress towards their goals
and so they themselves can see
their successes and growth over time.
And then it also gives the teacher a wonderful opportunity
to celebrate students' successes as they are progressing
towards that ultimate long term goal that you're working on.
Alright, so the next kind of strategy
that we wanna talk about briefly is vicarious experiences.
And the idea here is to help students observe success
of others who are similar to them.
And as Karen mentioned earlier, it's really important
that who the students are observing is similar.
It's not convincing to students that,
in a way that would build their self-efficacy,
if they're seeing adult success toward something.
They would need to see their peers
being successful at something.
So one way of doing this is using class demonstrations,
such as using a fishbowl activity,
and inviting students to be models during lessons.
And an important caveat here, that's a good thing
to remember, perhaps revisit that math anxiety deck,
is that you don't wanna put students in a position
where they're modeling in a way that would put them
in a place of creating a lot of math anxiety.
So you wanna be really mindful, or the teachers
would wanna be really mindful of that with the kids.
One way of sort of working on this is
to make sure that the teacher has posted and discussed
clear norms and expectations before beginning
any sort of class demonstrations,
especially if the students are going to be
asking questions and getting feedback of the peers
who are modeling, cause you want the discussion
to remain constructive, you want it to remain productive,
and to be focused on learning.
It's also really powerful to emphasize during demonstrations
that the goal is not just getting the right answer,
quote unquote, the big idea is that they're learning math
from observing and working with others.
It's not about just successfully
completing an algorithm and looking good.
There's a really nice example of a teacher lesson
doing a fishbowl at this blogspot URL,
classroomfruition.blogspot.com.
If you're unfamiliar with the fishbowl,
the general gist of it is that a small group of students,
usually, you know, four to six,
are seated in the middle of a circle
and all the rest of the students sit around them,
maybe in chairs, taking notes.
And the students in the middle are tasked
to work as a group, thinking and talking out loud,
to solve a particular math task.
And as they do that, the observers around the edge
of the circle can write questions
and at the end may be able to ask them.
But the idea it's that it's a way for students
to be showing that they're collaboratively working together,
and also that they are trying new strategies
that maybe the observers would not have tried themselves.
And just one note about that fishbowl example
at that blogspot address,
it is for a more challenging math lesson.
It's for older kids, so the structure and the idea
of the fishbowl is appropriate,
but they would need to change the math task
so that it's appropriate for your elementary aged learners
for the teachers you work with.
So another great way of building those vicarious experiences
is to make sure that the class has
a collaborative learning environment,
where students develop skills while observing their peers
and they're seeing other people model strategies.
And one strategy for doing this
is called Claim-Support-Question.
It's an instructional routine that was developed
by the National Council of Teachers of Mathematics.
And the original idea is that someone throws out a claim,
potentially the teacher, and the students work
in pairs or small groups to sort of test out the claim
and see if they can find support
for whether or not the claim is true or false.
And as they're working through that,
they might realize they have questions
they're not sure about, and so they make note of them.
So for instance, a teacher could start with a claim such as,
all multiples of nine are also multiples of three.
And then the students break into their groups
and evaluate, coming up with support to whether or not
they think that is true or false, find evidence for that,
and then make note of their questions they have.
At the end of the time period that the teacher them working,
they can all share their questions
of things that they didn't resolve together in their groups
and then they can have a discussion about that.
A final strategy for building those vicarious experiences
in classes is when you're having peer models,
students you have demonstrating their math work,
it's important to have some structured
guiding questions that teachers can deploy
that can help steer the conversation.
Because of course students are thinking out loud, even
thoughts that may not be productive or helpful can come out.
So the idea would be to use guided questions to help guide,
let the students not only make their thinking clear
and exemplify their thinking, but also give the teacher
a way to make sure that the students are attributing
their successes to things they have control over,
like the amount of practice they're doing.
So examples would be, if the student is working out,
solving a number sentence on the board, the teacher can say,
"Tell us what you know about this."
And point to a particular step, and then ask,
"How could you break this section here into smaller steps?
"How did you get from this step to that step?"
And based on that student's response,
the teacher knows whether or not they need
to try to redirect towards attributions
over which the student can control.
Alright, so the last piece of this self-efficacy puzzle
that we're gonna talk about today
is providing positive verbal persuasion.
And that really boils down to giving students
substantive, process-related feedback
that is specific and connects to their approach
that they've taken to the intervals
that they are trying to achieve
with the math problem they're working on.
So this is very much aligned with what we've termed
in other sessions growth mindset.
So in process-related feedback, the idea is to make sure
that you're using process praise that notes
the strategies and efforts the students are making
and to be specific about that, rather than commenting
on attributes of the student themselves.
So for instance, you could say something like,
"That was great work, Salome!
"You remembered to start by finding
"the greatest common factor for that equation,
"and then you were able to factor it out."
So this sort of feedback is not only praising their work,
their, you know, "great work, Salome", but also
very specifically calling out what it was
they did that was effective, which helps not only
build their self-efficacy but their growth mindset.
Another key factor, or trait I should say,
of process-related feedback, is that for it to be effective,
it needs to be honest and realistic.
When students hear undeserved or insincere praise,
they're not convinced by it.
And so it's also important that teachers
don't pretend that setbacks haven't happened
and that students aren't struggling.
Building up a student's self-efficacy is not pretending
that they are not encountering difficulties
and these things they need to grapple with.
So instead, it's important to acknowledge
the struggle that a student is having
and then highlight specific strengths
that could help the students cope with that struggle.
So for instance, you could say,
"I can tell you're frustrated, Lila.
"You're having a hard time solving this equation.
"I remember how last week you did a great job
"of following the right order of operations.
"I wonder if you can use that knowledge now."
This is an effective strategy, or excuse me,
effective feedback, not only because it's honest,
but also because it highlights to the student
what they've had success with in the past,
and highlights something that is specifically
something they can apply in the present
to solve the thing they're struggling with.
So it gives the student a little bit
of scaffolding in the mix.
Another great trait of process-related feedback
is challenging any negative self-talk that comes out
when a student is discussing their struggles
working over a math concept or a problem.
So for instance, if a student says
that something is too hard, the teacher responds, saying,
"Daren, I heard you say this is too hard.
"It's true that this is challenging,
"and you might not be able to do it yet.
"But I know you can if you keep at it.
"Let me show you a different approach that might help."
So we have a positive social persuasion scenario.
This is an activity you can do with teachers when you're
working with them in a group or even as individuals.
And the idea here is that we have a scenario
in which a teacher has noticed a student, Tyrone,
who's struggling with a particular math problem.
And so the teacher in this scenario maps out
what the teacher is telling the student and you're just
hearing the teacher's perspective on it.
And if you're working with teachers in a group,
you can have them identify examples of process praise,
examples of a student noting something
that is realistic or honest, and you can also see
if this teacher has made any attempt
at challenging negative self-talk.
And not all these things are present necessarily
in this particular scenario, and again if you'd like
to edit it to make it fit for your work, you're welcome to.
But it's just a little bit of practice for teachers
to identify those traits of persuasive feedback
that would be great for them to be able
to deploy in their own classroom.
In sum, another way you can wrap up this section
with your teachers, is to allow them some time
to reflect on which of those three practices or strategies
we just went through they are most interested in.
So is it mastery experiences?
Vicarious experiences? Perhaps social persuasion?
And then allow teachers to organize into groups
that have that shared common interest
and have a chance to talk to each other
about how they would build practice and seed practice
into their every day math instruction,
so they have a chance to not only talk about what they like
and don't like about it, but come up with ways
to ply their classrooms and maybe learn
from some of their colleagues that are also
in their small group, that might have different approaches
to incorporating these into their work.
Alright, and now I'm going to hand this back to Karen,
who will wrap it all up for us.
- Thanks, Lauren.
So we are at the end of our time together.
I wanted to spend some time today, before we say goodbye,
thinking about what all we talked about
across these four training sessions
and how they tie together.
I think one danger in having presented these
as separate sessions and have them separated across time
is it gives the impression that these are, you know,
very separate and isolated aspects of attitudes.
And of course, they are distinct from one another,
but they're very much interrelated as well.
And the four that we dove into, sense of belonging,
growth mindset, self-efficacy, math anxiety,
they have in common that they are part of
this basket of math attitudes and they are distinct
from one another but they very much have relations.
If we think about, for instance, growth mindset,
we talked about how the factors that can promote
growth mindset and we know that growth mindset can shift.
With practices that promote growth mindset,
we're really shifting to a classroom that emphasizes
learning and effort over performance.
And it's easy to imagine that
that might also impact math anxiety.
That takes the sting out of failure,
because we know in that classroom
that mistakes are actually welcome.
Likewise, if we think about how math anxiety
might be related to these other attitudes,
we talked today about how students
use their kind of physiological reactions to gage
their self-efficacy and those two things are related.
So if we are using strategies to promote
and help students come up--
help students to cope with their math anxiety,
we expect that to perhaps promote
greater sense of self-efficacy.
We also talked today about them,
how self-efficacy can be built by classrooms
that have more communal practices,
where students have lots of opportunities
to judge, watch their peers,
and see successes on the parts of their peers.
So if you each imagine in a classroom,
where we have to spend a lot of focused effort
on building a sense of belonging.
When students feel more connected
and have those relationships built with their peers,
then they're gonna be exposed
to their peers having more successes
which could in turn build their self-efficacy.
I think it's easy also to imagine links
between growth mindsets and sense of belonging.
When we feel capable of growth in an area,
we also feel probably more like a member of that domain.
And I've just talked here about ways I can imagine
these things being interrelated, but I think
that they are gonna be woven together in a complex way.
And I feel that to just make sure we're clear
and walk away from this training series by feeling
like when we promote any one of these things,
we're likely also to be promoting the others.
And it's time well spent.
I wanted to talk a little bit about these separate
training sessions and talk about the commonalities across.
You saw lots of slides repeated and some redundancies
across the different training sessions.
And this was not to be redundant
and waste your time, but rather for completeness.
Because, as we've talked about, a lot of these things
do carry over across to different math attitudes.
So some of the commonalities, you'll probably remember,
is each session we talked about the Farrington Model,
about how academic mindsets are important
because they promote behaviors
that also then promotes outcomes.
And so we tried to ground the sessions
in these four key academic mindsets to help give people
a structure for thinking about why we care about mindsets.
We find in our work around SEL,
that teachers often have a hard time
making a case to the higher-ups about the importance
of these non-academic, these non-cognitive factors.
And drawing back to this basic, kind of logic model
about why these things matter and how they promote
academic outcomes can be really powerful.
Other commonalities you probably have seen
across the different training sessions
was we focused on domain specificity.
So today when we talked about self-efficacy
we talked about how that's something
that students renegotiate for each different
domain and each different activity.
In the long one we talked about it's multi-dimensional
and domain specific, so in math students are not only
negotiating their sense of belonging with their peers,
but also with the domain itself.
"Do I belong in math?
"Is this a place I fit in intellectually?"
In growth mindset, we talked about how students
are gonna have different mindsets for different topics.
They might feel confident that they can grow
their language ability but feel less confident
about growing their math ability, for example.
We also talked about, in many
of the sessions, recursive cycles.
So today with self-efficacy we talked about
how self-efficacy can change how students respond
in the face of challenges and when they respond
more positively it could promote
the experience of mastery which further promotes
self-efficacy in a kind of circular way.
That hearkens back to what we talked about, for instance,
in math anxiety, where we talked about how,
when students are math anxious, they avoid math,
which leads to poor preparation,
which leads to poor performance,
which just further leads to more math anxiety.
We talked about a similar cycle when we talked about
sense of belonging and how, when students are unsure
about their belonging, it can get them into kind of
a negative loop where they are more vigilant
to cues about belonging, they interpret those cues
in the worst possible light, which only further
decreases their sense of belonging.
I bring up this recursive nature of many of these attitudes
because I think it points to how very important
breaking this cycle can be.
When we change our classroom practice
and use interventions to promote these attitudes,
it can be really powerful because it disrupts that cycle
and helps students reframe their experience
and their challenges in more adaptive ways,
that not only promote belonging but also are likely to
promote growth mindsets, self-efficacy, and lessen anxiety.
Another thing that's common across all of the sessions
was our focus on the potential for these attitudes
to be more likely to be problematic
for students that are historically marginalized.
We focused a lot on gender and how there's something unique
about math that sets girls and women up to be less confident
in their abilities and hold more negative attitudes.
And so in each of the sessions we talked about why math
is a unique domain because it comes
with some pre-loaded baggage about stereotypes
about who's expected to be good and the kinds of abilities
that girls are expected to have.
We hit on this in each of the training sessions
because we want to make it clear that there's a likelihood
that these interventions and classroom practices
can be particularly effective in helping serve
marginalized students and promote more positive attitudes.
We want you to take away from this training series
that these sessions are very much intended to be modular.
We have repeated these commonalities
across all the sessions, but we want you to feel like
you have a license to take them
and break them up in ways that suit your needs.
So for instance, if you did more than one training session
in a day with a group, you might want
to reduce some of that commonality.
You might also want to add or exclude activities
as is appropriate to your setting.
And we want you to feel comfortable doing that.
What is next?
Well, from us you can expect I'll be in contact
with each of you individually to talk about clock hours,
paperwork, and if that's something
you would like us to complete for you.
We will also be in touch when we have
a final revised set of these materials for you.
I've mentioned this throughout, but we have been taking
the feedback we've received from you and also things
we've learned, lessons we've learned in presenting
on these materials, and we've been tweaking
the materials and ways to improve them.
And we wanna share those back with you
once we've completed those revisions.
There is something that we need from you,
and that is your feedback.
We are required, when we provide clock hours,
to solicit feedback from trainees.
We are also required from our funder,
The Institute for Education Sciences, to get the feedback
of people that we work with in our trainings.
So we would like to respectfully request that you complete
a feedback survey that I will be emailing out tomorrow.
I'll send this around with a link to the video from today,
if anyone had to enter late,
or for a colleague that missed it.
I'll send that link out but I'll also
give you a link to the survey.
We really really really hope
that you will consider responding.
Your feedback is very important to us
and we will use it in our work moving forward.
And it's very important to our funder as well.
So look for that email tomorrow
and maybe a pesky reminder or two in the days to come.
We really appreciate you taking the time to do that.
Now we have just a few minutes before we need to head off
and I would like to spend some time, if you are willing,
thinking about the training series
and doing a little bit of reflection.
And if you have access to your chat, Lauren and I would love
to hear from you, your thoughts
on either of these questions.
The first, what stood out to you,
what's increased your knowledge or changed your thinking?
And that doesn't have to be from today's session,
it could be across the training series.
And importantly, we're also interested in your input
about what would be additional support
that you feel would be useful?
Now, having been through all four of these trainings,
is there anything you wish, "Oh gosh, I really wish
"they would have talked about X
"when they talked about sense of belonging."
So if you have any thoughts on either of those questions
and you feel comfortable sharing them in the chat,
would you please do that now?
We'll take a minute and give people time to think.
And if you could chat to all participants,
if that's an option in your chat box, that would be great.
You are a quiet bunch today; I will take that
as a good sign, that you're thinking deeply
about all that we have imparted to you
over these last few months together.
Not to worry, you'll have plenty of opportunity to share
thoughts with us when we send you out the feedback survey.
I think that is it for us today.
We do hope you keep in touch, we'd love to hear
if you use these materials with your teachers
and have any feedback or questions.
We are more than happy to take those,
we'd love to thought-partner with you if we can support
your work in any way on using these materials.
You have my email address and I'm happy to share
the other team members' with you.
But in the meantime, keep in touch, keep doing good work.
And we will send out an email shortly with a link
to the video and getting your feedback on the survey.
Thanks everyone!
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