Life In Intervention
Welcome! Please find a seat anywhere in the room
Please grab a notecard from the table and write the
following:
1. Your Name
2. Where you teach & Which courses
1.
If you teach an intervention class, how many students are in it?
A question that starts with “How do you handle it when a
student …?”
4. The most important thing you’d like to walk away with
from today and bring back to your classroom
3.
Introductions
Let’s Get Started…
I Am: Dan Schneider
I Teach: Math Intervention @ Amphi High School
I Graduated: U of A Secondary Math Education
Program, class of 2011
I Write: http://mathymcmatherson.wordpress.com
Introductions
Let’s get to know who’s in the room too…
Please be ready to share:
 Your Name
 Where & What you teach
 Your “How would you handle it when a student…”
question
Introductions
Moving forward in our time together, I’d also like to
know your students – the ones who need the most
help or who are the most challenging.
Right Now
Think about these students and their behaviors,
the content that they struggle with,
and things you hear them say to themselves or to you
(their quotes)
Introductions
The Activity
At your table are stacks and stacks of post-it notes.
Start writing down your thoughts on these post-its.
Write as many as you can come up with.
Once you’ve exhausted your brain, walk around the
room and put them on the posters labeled
Behavior, Content, and Quotes
After you’ve placed your own, start reading what others
have already written
Regrouping
Observations
An Intervention Student
 Low Skills
 Makes mistakes with the fundamentals – positive vs
negative, multiplication tables, etc
 May feel like they understand the lesson during class,
but when they do the homework, they get every
question incorrect
 Usually also has low confidence in math
 The Strategy: Give them a model to fall back on that
they can use for their fundamentals
An Intervention Student
 Low Effort
 Afraid to take risks
 Has lots of deflection strategies to avoid doing work

No pencil, no paper, “Can I use the bathroom?”
 Needs a lot of hand-holding through problems
 Doesn’t know how to use notes/resources for help
 Can’t see how problems are related; feels like every
problem is ‘brand new’
 My Strategy: Be firm & patient; Use questions when
working together; Consistent Expectations
An Intervention Student
 Answer-Getting
 Blurts out answers
 Turns in assignments incomplete or incorrect
 Is compliant when taking notes or doing problems with a teacher;
disruptive during ‘investigations’ or ‘class discussions’
 Doesn’t show work
 “I’ll do it because the teacher told me”; learn for the test, then
forget
 May have passed their math classes, but their skills aren’t where
they need to be
 My Strategy: Force this student to come to terms with what they
know and don’t know through my grading & assessment system
Outcomes for Today
 I hope you leave here with:
 Classroom strategies you can start trying tomorrow
 Resources you can start using in your room tomorrow
 Grading strategies for you to consider this year or next
year
 Ideas to take back to your administration on how to
better create & fill intervention classes
Structures for Today
 Content Resources
 How I’ve taught: Integers & Algebra
 How I think about teaching other fundamentals
 Process Strategies
 How I work with students 1-on-1
 Lesson structures I use to discourage passive learning
 Culture Shifts
 How I use my classroom space to encourage success
 How I use grading & assessment to promote shifts in
student effort & motivation
Mindsets
Consider the following two statements:
“Intelligence is something that can grow or
change with effort”
“Everyone has a certain level of intelligence – the
best I can do is already fixed for me and, no matter
how hard I try, it can’t be changed”
By Yourself: Which one do you find yourself agreeing with?
Mindsets
With Your Table:
How do the people at your table feel?
Anyone have a story that seems to support one or the other?
“Intelligence is something that can grow or
change with effort”
“Everyone has a certain level of intelligence – the
best I can do is already fixed for me and, no matter
how hard I try, it can’t be changed”
Mindsets
Mindsets
Growth Mindset
Fixed Mindset
 Belief that intelligence is
 Belief that intelligence is
dynamic
 Belief that, with effort, we
can learn new things
 “The growth mindset is
based on the belief that
your basic qualities are
things you can cultivate
through your efforts”
static
 Belief that we either know
something or we don’t
 “Believing that your
qualities are carved in
stone – the fixed mindset –
creates an urgency to prove
yourself over and over
again”
Mindset Reading
 The modern idea behind Mindsets was established
by Carol Dweck & her book Mindset
 There are both neurological studies and research-
based trials that support the idea that a believing
in a growth mindset can fundamentally
change how you learn
 Let’s do some reading…
Mindset Reading
 Here is a sample from parts of Dweck’s book.
Please read the following sections:
 P. 16 – Is Success about Learning – or Proving you’re






Smart?
P. 17 – Beyond Puzzles
P. 18 – Brain Waves Tell the Story
P. 32 – Mindsets Change the Meaning of Failure
P. 42 – High Effort: The Big Risk
P. 57 – Mindset and School Achievement
P. 58 – The Low Effort Syndrome
 Underline four passages that you think help explain
some of the behaviors or quotes we have on the wall
Table Sharing
The Task
As a table, decide on 2 quotes that you think are the
most relevant for working with an intervention student.
Once you’ve decided, choose someone to write them on
one of the large whiteboards around the room
Mindsets in My Class
 As I was preparing this presentation, I realized that this
idea of a ‘growth mindset’ is underlying every aspect of my
class:
 How I scaffold content
 How I give feedback and praise
 How I structure my bellwork/homework procedures
 How I structure my gradebook
 How I work with students 1-on-1
 I do this purposefully – I want to change the mindset
of my students
Mindsets of our Students
 “I think that the smart people are just born smart. The
people who have trouble with math – I guess we weren’t
lucky. I guess we were born with less intelligence. I just
wish I was smart”
 “My self motivation is actually low. Because I thought I
was so stupid, I didn’t give myself motivation. My
grades were good but my test scores were horrendous”
 “I’m always that student who has a question but is too shy
to ask because of fear that people will think I’m more
stupid than I already am”
 “The teacher expects us to understand it in our first try”
Mindsets of our Students
 “Sometimes they are taught too fast. I always struggle with
math but I think if I put effort into it I will learn it”
 “With effort, determination, and time your math skills
can improve”
 “I know I’m capable of doing it, it’s just a matter of effort
I put into my work. I know I need dedication & faith”
 “I want to try my hardest to prove to myself and everyone
that I’m able to do it”
Shifting Gears
 Let’s start talking about some math that we probably all
teach: Integers
-5 – 8
-6 + 9
3 + (-6)
7 – (-4)
Questions I Wrestled With
 How do you teach integers with a foundation that isn’t just
a series of rules to memorize?
 How do you explain your reasoning in a way that doesn’t
rely solely on a rule or a “me vs you” argument
 How can I give students a scaffold to rely on so they can
check their answers without confirming it with me?
 How do I navigate the conceptual waters of “negative” vs
“subtraction”, especially knowing what they will see in
coordinate geometry and algebraic manipulation
Number Line Model
 Numbers Are: Movement on the Number Line
(Forwards & Backwards)
 Operations Are: Directions you Face when Moving
 You Solve problems by: Drawing on a Number Line
 Real-World Counterparts: temperature, traveling
between places, altitude
Number Line Model
-5 – 8
-6 + 9
3 + (-6)
7 – (-4)
Physical Model
 Numbers Are: Physical tokens with ‘opposite’ values
 Addition Is: ‘Bringing Objects Together’
 Subtraction Is: ‘Taking Objects Away’
 Solve Problems By: Drawing pictures & crossing
things out
 Real-World Counterparts: Money, holes & piles,
tokens, physics (electrons vs protons, hot vs cold)
Addition: “Bring Objects Together”
3+4
2 + -5
-3 + (-4)
-6 + 2
Subtraction: “Take Objects Away”
7-2
1-4
-7 – (-2)
-2 – (-5)
Some Comments
 Pros:
 Visual model with dedicated procedure for students to get
the right answer every time
 Both lead to same set of ‘rules’ that we eventually memorize
 Cons:
 Two different meanings of negative sign
(subtract vs negative) – need to remember which one to use
Additional Issues
 Our students are not blank slates: they walk into the
classroom already having seen these problems before
 And, even worse, they have incorrect rules halfway
memorized
Me!
Integers
Algebra
Fractions
Multiplication Tables
Long Division
Teaching Sideways
 When I want to design a coherent curriculum to
tackle these issues, I find myself using the term
‘Teaching Sideways’
 The Goal:
 Present a task or situation or puzzle that seems unrelated to
anything a student has ever seen before
 Investigate the problem in such a way that it would seem
like there’s a strategic way to solve the problems
 In trying to discover this strategy or represent the problem
precisely, discover the math hidden underneath
Teaching Sideways
 When I want to design a coherent curriculum to
tackle these issues, I find myself using the term
‘Teaching Sideways’
 Advantages
 Cuts out the ‘I know how to do this already’ dismissal
 Cuts out the ‘I remember doing this and hating it’ dismissal
 Cuts out the ‘I HATE FRACTIONS MATH’ dismissal
 Builds a new foundation that will eventually override and
replace the old, incorrect foundation
Putting Practice into Action
 Here’s what we’re going to try: I’m going to teach you
integers – how to add & subtract them.
 I’m using the exact lessons & worksheets that I use in my
own class. I’m going to teach it just like I would teach it in
my own class.
 You can download all of these from my website at the end
of the day
Putting Practice into Action
 The Purpose:
 Create some discussion points around ‘How would you
handle…’
 Lead into some talking points about the process that I use for
certain things
 Lead into some talking points about the culture I create in
my class around these lessons
 Demonstrate some of the strategies I use to avoid ‘passive
learning’ or ‘non-responsive’ learning
 Your Job:
 Stop being a teacher – start pretending to be like your
students
Things to Notice
 There is always a procedure
students can fall back on to
guarantee they get a correct
answer
 Questions ask for
explanations rather than
answers
 Questions require students to
display their thinking in their
answer
 Answer Banks for immediate
feedback
 Complete some problems,




but they must be correct
 Really effective for the
‘answer getting’ student
Displaying independent work
expectations
Asking them to reflect on
comfort level before and after
lesson
Analyzing mistakes is explicit
in the curriculum
Bellwork procedure helps
normalize mistakes
Feedback in: Bellwork
Feedback in: Bellwork
Lesson & Problem Design
 Choosing which problems to complete, how many, and
in what order is a big deal, especially if I want to create
a catalyst where a student has the opportunity to really
learn something and shift their mindset.
 The Question: How can I design a task that:
 Teaches students how to complete a problem
 Make sure they know it before continuing?
 Let’s the student receive feedback and feel confident in
themselves?
Lesson & Problem Design
 A Video!
 Edmund McMillan discussing how he designs levels for
his game Super Meat Boy
 Every time he says ‘level design’, consider: ‘task design’ or
‘lesson design’
Questioning
 If I’m on my A-game, then I should have asked a lot of
questions during these lessons
 Asking good questions is something I work really hard
on. None of it is accidental.
 I want to share one of the more influential things I’ve
read that informs how I ask questions and work with
students 1-on-1
Never Say Anything a Kid Can Say
Right Now
Read from Questioning Strategies that Work for Me,
but stop just short of Participation is not Optional
Underline any strategies that you saw me do or any
strategies you’d like to steal for your own use
Never Say Anything a Kid Can Say
Discuss
What lines stand out to you as especially important or
insightful?
Do any lines help answer a ‘How would you handle it
when…” question?
Never Say Anything a Kid Can Say
Right Now
Read the rest of the article on Participation is not
Optional
Underline any strategies that you saw me do or any
strategies you’d like to steal for your own use
Never Say Anything a Kid Can Say
Discuss
What lines stand out to you as especially important or
insightful?
Do any lines help answer a ‘How would you handle it
when…” question?
Questioning Practice
The Activity
I’m going to pretend to be a student in your class
You’ve given me an integer problem to complete and
I’ve made a mistake
The Task
What questions would you ask to
help understand what I’m thinking?
What questions would you ask to
help me realize my mistake?
Questioning Practice
-3 – 5 = -2
Questioning Practice
-3 – 5 = 8
Questioning Practice
5 + 7 = 13
Questioning Practice
-10 + 15 = -5
Questioning Practice
-5 + 6 = ?
Your Turn
The Activity
You are working with a student from a Geometry class who
has been struggling all year. After doing some preassessments, you notice that it seems like its their integers
that are the main problem. This student is low-skilled
and, because they’ve been unsuccessful all year, they don’t
put forth much effort anymore. They’ve seen integers
before, but seem to have lots of rules memorized and
don’t know how to use them. They don’t have any issues
focusing when working one-on-one.
Someone In This Room Will be Playing the Student
Your Turn
The Task
While working 1-on-1, you can give the student no more
than 10 problems or questions to answer. But, by the
end of these problems, two things should be
accomplished:
 You should know how the student is thinking about
integers (and hopefully now it’s a correct way)
 The student should feel more confident about how well
they understand integers
Your Turn




The Goal
Get some practice asking probing questions
Get some practice asking questions as an alternative to
telling
Emphasize the importance of you, the instructor,
choosing the right questions for the right time
I’ve always wanted to try this: have teachers pretend
to be the trouble students and see what conversations
this generates. I hope it isn’t a disaster
Picking Problems
Right Now
On a sheet of paper, design your 10
questions/problems/tasks to help you investigate your
students’ knowledge
Once We’re Done
We’ll find partners and take turns being a ‘struggling
student’ and a ‘questioning teacher’
Small-Group Strategies
 Claim: Creating opportunities for students to work in
small groups allows me to work 1-on-1 more frequently
with students, which lets me create the most impact
on my students
 Two Strategies:
 Expert Groups
 Group Whiteboards
 Your Strategies?
Expert Groups
 (Based on the concept behind a Jigsaw)
 Every group gets a specific problem which is
intentionally complex
 Ideally, there’s around 6-8 groups
 The group has 20 minutes to work through the problem
on a group whiteboard
 It’s important that the surface can be erased
 Their goal: become the experts on the problem in front
of them
 During these 20 minutes: I help in whatever way I can,
even if it means explaining everything from scratch
Expert Groups
 After 20 minutes: Each person gets a worksheet with
all of the problems on them, including the one they just
did
 And all their work is erased from the whiteboard
 Their task: complete all of the problems on the
worksheet
 And remember: you’ve already done one! The rest are
similar!
 But – if you get stuck: find one of the expert groups
and ask them for help!
 My job: facilitate people helping each other
 An Example
Group Whiteboards
 Each group gets a large whiteboard, a marker, and an
eraser
 The Rules:
 Only one person can write
 The person who writes cannot speak
 The person who writes may only write what someone in
their group has said out loud
 After every problem, the whiteboard rotates
Group Whiteboards
 Eventually: a struggling student will get to hold the
marker.
 And that student will complete the problem because
their group has helped them
 And now I get to say: “See! You did it! You can do these!
No more excuses!”
Your Strategies?
Some Topics on Culture
 Here are a few things :
 Normalizing Mistakes


Bellwork
Games
 Classroom Decorum
 Culture of Immediate Feedback
 Exit Tickets
 Wall of Problems
Normalizing Mistakes: Games
 Pico, Fermi, Bagel
 The Rules: I pick a 3 digit number, you try to guess it
 I will respond in one of 3 ways:



B = none of the numbers you guessed are correct
P = 1 of the numbers you guessed is correct, but in the wrong spot
F = 1 of the numbers you guesses is correct and in the right spot
 You Win If: I respond with FFF
PFB



B = none of the numbers you guessed are correct
P = 1 of the numbers you guessed is correct, but in the wrong spot
F = 1 of the numbers you guesses is correct and in the right spot
Normalizing Mistakes: Games
 Pico, Fermi, Bagel
 Why I Play this game: You HAVE to make a mistake
 The fundamental premise of the game is that you make a
mistake and try again. How cool is that?
Normalizing Mistakes: Number Puzzles
Normalizing Mistakes: Number Puzzles
Normalizing Mistakes: Number Puzzles
 Why I Like Them:
 Most students will start by guess and check
 But – the checking involves checking the puzzle for
consistency


Once I put in my answer, does it satisfy the puzzle?
This is a very real problem solving strategy that is tricky to
teach
 Side Note: I’ve considered using these puzzles as a way to
teach Systems of Equations
Role of the Classroom
Role of the Classroom
The Role of Feedback
 Feedback is best given:
 As a mistake is happening
 In a way that causes the student to reflect on the mistake
so they can avoid it next time
 An Important Question: What structures do you
have in your classroom that:
 Allow students to get immediate feedback from you?
 Allow students to give themselves feedback & be
reflective?
 Allow students to make mistakes in a way that is okay?
Feedback and: Exit Tickets
 Instead of last 5 minutes for homework:
last 5 minutes for Exit Ticket
 Advantages
 Lets students know what is expected by the end of class
 Lets students who get bored have something to work on
 Gives me immediate feedback in case a student tries a
problem ahead of time and gets it wrong
 Different things I’ve tried:
 Having Exit Ticket written on a side whiteboard
throughout entire class
 Having Bellwork on one side of a quarter-sheet; Exit
Ticket on the other side
Exit Tickets
 As class is ending:
 I walk around and check the exit ticket


If they’re correct, I collect them.
If not, I say ‘nope – check #___ again’, then move on – don’t linger
 After a while, there may be a few students who haven’t
completed it


I can work with these students a little more closely, or:
They ask for help from one of their neighbors, who has to reexplain it because I collected his/her exit ticket
 When class is over:
 I know which students I need to check in with during
Bellwork tomorrow
Exit Tickets
 Advantages
 Not optional
 I know what students have done
 Helps me plan for the next day
 As opposed to:
 ‘I’ll just do it at home – it’s fine’
 I’m guessing what students took away from the lesson
 Some food-for-thought:
 If your school’s demographic is in the lower SES range,
then most of your students live in the now.
So – why not make them do their problems in the now
too?
Working With Students
 The Problem: I know a student doesn’t know how to
do something. I need them to learn it.
 My Goal: Create a catalyst moment between me and
the student
 Finding the right problem for the right moment and
being their at just the right time so I can fix it
 For me: these usually happen during bellwork, during
Exit Tickets, or during group activities
 A Consequence: I need lots and lots and lots of
problems that I can pull from to use with students
The Wall of Problems
The Wall of Problems
Problem Resources
 One of the most valuable uses of my time has been
collecting problems
 http://www.worksheetworks.com/math
 Kuta software

https://www.kutasoftware.com/
 Geogebra (for generating Geometry diagrams)

http://www.geogebra.org
Why So Many Problems?
 My Theory: It takes 5 problems for a student to be
able to do a problem confidently
 1 Problem for me to do while explaining to the student
 1 Problem for me to do while I ask the student questions
 1 Problem for the student to do while I ask them
question
 1 Problem for the student to do while they ask me
questions
 1 Problem for the student to do and ask
“Did I get it right?” at the end
A Little Break
 How we doing? Need a break?
 Here – let me hand out some puzzles for us to
consider…
The Puzzles
The Puzzles
The Puzzles
 See if you can finish them…
Surprise!
 The puzzles are secretly Algebra!
Some Notes
 Visual way to reinforce importance of the equal sign
 Creates a way for students to explain their answers in a
way that isn’t “my word vs yours”
 Verbal cue to start problem
 “Draw a line through the equal sign”
Grading & Assessment
 Now that you’ve seen how I teach integers and algebra,
let me show you how I assess it…
 (I should be passing something out now)
Standards Based Grading (SBG)
 I use a process called Standards Based Grading
(SBG) for my intervention classes
 I also tried doing it with my geometry classes for a year
with mixed results
 SBG has several components, including:
 Isolating particular skills or standards and representing
them in your gradebook as such
 Repeated assessments on skills, both given in class and
student initiated
 Holistic grading on a rubric
Standards Based Grading (SBG)
 Why I use SBG:
 Dismisses some of the ‘Test Anxiety’ fear – short quizzes
instead
 Allows students to retake assessments as many times
as they need
 Students aren’t given a ‘grade’ – they’re given ‘feedback’
which they use to plan their next move

Which is secretly a grade, but this distinction has a
psychological effect
 Isolates skills so students know where to focus
Standards Based Grading (SBG)
 How I Grade Them
 I should be passing out the rubric that I use with my
students
 I’m also going to go through the verbatim lesson I use
when I tell students about this way of grading
The Growth Mindset
Each sticky note is a
student who earned a
5 on one of my skill
quizzes
The different colors
represent different
classes
The Growth Mindset
SBG and Test Retakes
 In every class I’ve every taught, I’ve always allowed a
student to retake a test as many times as they want
 The Advantages:
 Students don’t feel like there’s a ‘dead end’ in front of
them. Retakes always provide an opportunity to change
how things could turn out
 I can grade some items harshly because I know a student
can come back and retake it

This is incredibly important for remediating basic skills
 It provides an opportunity for students to reflect on how
they did on the last test and why; correcting behavior
SBG and Test Retakes
 Retake Contract – pass out
 Tutoring Contract
 Tutoring Skill Checklist
 Observation: The personal invitation is important and
sometimes all you need
 The more you can isolate specific skills for a test, the
easier it is for a student to take ownership and retake the
test
Struggles of SBG
 I’m pro SBG, but there are some downsides:
 Lots of test retakes to generate
 Skills become isolated, making it harder to test the ‘higher
order’ skills that students need


My response: intervention classes are supposed to fix isolated skills,
which can then be used in the more complicated problems in a
regular class
And: use a project/presentation to assess seriously complex skills,
not a test
 Lots of pressure to create the right test and choose the
right skills
Choosing Skills of SBG
 When I design a unit and try to break down the skills, I
think of:
 What are the fundamentals of the unit that a student
needs to know before moving forward? Make these their
own skill
 What is the finish line I want a student to reach? Work
backwards to decide on skills that support reaching this
finish line
SBG Skills for Algebra Unit
 Finish Line:
-2(3x + 4) – 6(2x – 9) = 3(4x + 8)
SBG Skills for Algebra Unit
 Previously:
 Adding & Subtracting Integers
 Multiplying & Dividing Integers
 Skill 1: Solve Basic Equations
 Skill 2: Solve Equations – Combine Like Terms
 Skill 3: Solve Equations – Distributive Property
 Skill 4: Solve Equations - Proportions
Designing SBG Tests
 Tiered Approach:
 Decide on ‘minimum levels of understanding’ and design
problems around those levels. Works well for skills that
build in complexity’
 Consistency Approach
 Pick enough problems of a similar type to make sure the
student is being consistent
 All or Nothing Approach
 One or Two problems of the highest complexity – credit
awarded based on how well they used different strategies
to solve the problem
Designing SBG Tests
 Schneider passes out another SBG test he used when he
taught Geometry
SBG: You Try
 You are designing a unit on Graphing Lines. By the end
of it, students should be able to:
 Graph a line given an equation in any form
 Given a graph, write the equation of the line in slope-
intercept form
 Given an equation or a graph, write the equation of a
parallel and perpendicular line
 The Question: What skills would you assess your
students on? What would a sample question look like?
 Fill this in on the bubble sheet you were given earlier
Graphing Lines SBG
Shifting Gears
Dedicated Intervention Classes
 The Team:
 A teacher
 An administrator

At Amphi: School Improvement Specialist
 A counselor
 My Belief: Important to have someone on the
administration who:
 Also cares about the students
 Can be someone to talk to who isn’t the teacher
Dedicated Intervention Classes
 Identification: Lots & lots & lots of data
 The Goal: Make students aware of their need for help
 The Goal: Make students realize people are paying
attention and there are consequences
Dedicated Intervention Classes
Dedicated Intervention Classes
Dedicated Intervention Classes
 The Process:
 Meet with the students as a group and explain why
they’re here and what the opportunity is
 Have them take a skills survey as one final piece of
data to see what they know and what they don’t
 If there’s ever anything they need to take seriously, it’s
this survey
 If all the data still points to an intervention: they get a
letter saying their schedule will be changed and they
end up in an intervention class
Dedicated Intervention Classes
 The Class
 12 students max (research-based number)
 Standards-Based Grading
 No ‘unit tests’ – skill quizzes on isolated standards
 No credit recovery
 Counts as an elective credit
 Curriculum: (1) Integers, Algebra, & Graphing, (2)
Support their current math class
Dedicated Intervention Classes
 A Personal Opinion
 Sophomores are the best candidates for a true
intervention class
 They’ve started to mature out of freshman year, which
will continue when they get their Drivers license
 They’ve experience consequences

Failing classes, discipline issues, etc
 They haven’t fully committed to deciding what kind of
student they’ll be
What Else?
Other Things
 You can find me:
 dschneider@amphi.com
 www.schneiderisawesome.com
 http://mathymcmatherson.wordpress.com
 Twitter: @mathymcmatherso