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Welcome everyone to the Ontario
Association for Mathematics Education

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conference and to our presentation
"Raising the Level of Numeracy and

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Preparing Students for Success in High
School and Beyond. My name is Emily Brown

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and I am a mathematics professor at
Sheridan College.

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Good day everyone. My name is

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James Howell. I am the manager of
academic partnerships at Vretta Inc.

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Thank you for joining us today.

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So on
today's agenda we're going to have the

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initial challenge that prompted a look
at college math grades and a look back

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to high school and secondary mathematics.
We're going to be looking at the College

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Student Achievement Project data and the
Assessment Development project and we're

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going to look at the Ontario Colleges
Math Test timeline and deployments.

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The Assessment for Learning app for
secondary school students. The OCE

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research project and results and of
course as always you can contact us with

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any questions or for further information.

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So it is known that Canada has a
significant numeracy gap where from OECD

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and PIACC and PISA data, we see that
almost 55% of Canadian adults are below

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the desired and functional level of
numeracy. You can see from 2006 to 2015

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where Canada was ranked amongst other
countries around the world. From 10 years

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of data, looking at college student
mathematics grades and successes, it was

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noted that a third of students were at
risk of not completing their college

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program due to their grades in first
semester mathematics courses. Here this

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slide shows a summary of all programs.
Almost forty thousand students and then

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broken
down into the different programs. Applied

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arts. Business. Foundations. General
studies. Human services and technology.

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So what happens when we look at college
student attrition? If we have a 100%

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of students going into their
first semester math courses, we see that

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those with good grades and continue on
to a second semester number 68% and of

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those continuing on to winter semester
we have about 25,000 students. The third

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that are at risk and continue into the
second semester number 60% and not

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continuing number 40% of
students. So we can see that 40%

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of those students who are at
risk simply discontinue their college

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studies. In 2004, the College Student
Achievement Project was initiated as a

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joint project by the Ministry of
Education and the Ministry of Training,

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Colleges, and Universities. This project
reviewed the high school student success

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once they attended college mathematics
courses and then reflected back on the

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achievement of the students in high
school - what courses they took and so on.

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After ten years of reporting declining
data and a consistent third of students

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at risk of failing their college
programs because of math achievement, the

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ministries suggested that we look at a
common math assessment. So a common math

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assessment was developed testing the
common concepts that were discovered in

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first semester mathematics courses and
then field trialed with over 10,000

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students across 16 colleges and in 112
secondary schools in Ontario.

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Key numeracy concepts that were assessed are
those that are initially introduced to

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students in the Ontario curriculum up to
grade 8. While a third

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of overall students are at risk of
failing their college programs because

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of their math skills, in fact it can be a
lot worse depending on the high school

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course that students took. So in this
particular slide we're looking at

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students who studied MAP4C and overall
40% were at risk of not achieving their

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goals in their first semester
mathematics courses. And also the other

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columns indicate that not only does the
course impact their success but also the

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grade that they achieved in this course.
So here you can see that if you achieved

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over 80% in MAP4C, you are more
successful with 76.6% achieving good

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grades in their first semester college
course. With grades from 70 to 79%

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in MAP4C, it dropped to 62.5%
achieving good grades in their college

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math. And again with lower grades in MAP4C between 60 and 69%, only

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47.6
were achieving good grades in their

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college math courses. The same patterns
were observed with other high school

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math courses. For example MCT4C and
other college math or other courses that

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were prerequisites for for these
programs. So if we look back earlier in a

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student's math journey to their grade 9
and 10 course selections, it is also

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related to their ultimate to their
college achievement where students who

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take academic courses in both grades 9
and 10, which is the most common route,

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they have the highest level of
achievement in college mathematics.

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For example, here from the chart you can see
that those who were in academic achieved

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good grades at the rate of 76.2%.
When you look at the students

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who take an applied course and then
follow that up with an academic course,

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the 67.1% achieve good
grades in their college courses. But the

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target group for this presentation
really is the students who take grade

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9 and 10 applied, and you can see in
the first column that they are almost at

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48% at risk of not achieving in their
college math programs due to poor math

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skills. So if we look at the timeline, the
project began in 2004 with the joint

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funding from the two ministries. In 2011
the ministries expanded their scope to

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include language as well as mathematics
and some similar gaps were noticed as

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well in that data. So at that time the
project went from College Math Project

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to being called the College Student
Achievement Project. In 2013 two

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projects were launched, two partner
projects and that was the Assessment

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Development Project - to develop a common
math assessment for the college system,

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as well as a common learning outcomes
project. In 2015 once the assessment was

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fully developed and field tested, Humber
College launched a public RFP in order

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to find an implementation partner and
Vretta was named the successful vendor.

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In 2016 the OCMT was implemented for
post-secondary post admission placement

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testing and that was primarily tested at
Humber College before being offered out

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to other colleges. In 2016 an award was
granted to Humber, the Toronto Catholic

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District School Board, and Vretta under
the Advancing Education Program to adapt

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the Ontario Colleges Math Test for that
high-risk group, the grade 9 applied

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mathematics. In 2018
Addressing the Numeracy Gap, a final

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report
from that award grant was published

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showing the results on research joining
the EQAO scores with the final grades in

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math and correlating that to the OCMT
usage.

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Okay, so thank you so much for that

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timeline summary there Emily. I'm just
gonna take a moment to discuss the

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deployments at the college level as well
as addressing the numeracy key gaps

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study that I had the pleasure of
participating in. So in 2015 and 2016

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when the test was first deployed for
post admissions, it was delivered through

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test centers in a proctored environment
face-to-face and online through

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third-party proctoring systems and the
results of the tests that students took

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would determine which first-year math
course they took, whether it be you know

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4 teaching hours per week course, or
3 teaching our four-week course, or

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directed studies. The test was designed
to take no longer than 60 minutes and it

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would include questions from all of the
9 foundational numeracy topics that

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were identified by the CSAP project. In
addition to the post admission placement

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test, the OCMT was also deployed for
apprenticeship programs as well as

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academic upgrading. In these environments
it was also delivered in a proctored

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environment to diagnose those students
and address their gaps and then they

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would work closely with the academic
upgrading department to work through the

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CSAP modules and get that one-on-one
support they needed for continued

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success. Also in 2016 I had the pleasure of being

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involved in the Advancing Education
Program with funding through the

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Ontario Centres of Excellence to adapt
the OCMT platform for students in

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grade 9 specifically applied mathematics.
This deployment involved the TCDSB as

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well as Humber College and myself from
Vretta.

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As mentioned before we were looking at
using the upgrading modules as well as

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the assessments both as a diagnostic as
well as a post-test or summative to

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assess that level of mastery. Data from
this would be correlated with usage and

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the students would be tracked, the EQAO 
scores as well as their final grades in

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these mathematic courses. So here we can
see the numeracy concepts covered within

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the secondary school system application.
On the right here we have the 9

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different numeracy concepts covered in
the tool. We have whole numbers, number

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sense, integers, decimals, fractions, ratios
and proportions, percentages, algebra, as

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well as conversions. All of these areas, sorry these concepts, have their own

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diagnostic as well as upgrading modules
tied to the diagnostic and then

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a cumulative summative test which would
reassess the mastery. This platform was

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developed to be delivered through iOS
devices and as you can see here this is

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what it would look like to a student
accessing the system from a tablet.

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The three phases as I just briefly touched
on there are to diagnose in a specific

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topic area, identify the skills that the
student has potential gaps in before

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giving them targeted upgrading which
would allow them to practice those

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concepts and achieve mastery in them,
before reassessing the numeracy

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knowledge of that student and in the
summative test at the end.

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First phase of this tool begins with the
diagnostic assessment. The same

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assessment framework for the college
system was followed in the OCMT app.

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It looked at those 9 foundational
numeracy area topics and it also looked

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looks at the performance expectations
for the broader goals in operating in

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mathematics. Those are A - Knowing, B - Applying, and C - Reasoning. Similar to

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the college assessment, all of these
assessment items are given multiple ways

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of submitting answers in both multiple
choice as well as written response types

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and all of these items were
psychometrically validated as well as

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field tested. The diagnostic assessment
is also designed to be unique for every

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test taker and equally representative of
both the content in those nine

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foundational topics as well as you know
equally representative of those three

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different performance expectations. The
college system as we spoke about before

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was designed to be given in a proctored
environment in 60 minutes and the

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diagnostic does follow that initially.
However we found through adapting this

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for schools that one single diagnostic
was taking too long for grade 9

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applied students. So during the project
we adapted this assessment framework and

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we broke those nine different topic
areas into distinct diagnostic

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assessments. The idea here was to make it
long enough to diagnose those concepts

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sufficiently and to be given short
enough within a single period of a

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mathematics course at secondary school
typically 75 minutes. The upgrading

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modules take those nine foundational
topics and they break down the larger

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concept based on those performance
expectations and they really engage

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students into taking micro steps
to work their way up to the larger

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concept. There's different interactions,
little games you know activities for

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students to do. These are not static
videos. They're really engaging to make

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students to help them master these
concepts. And the goal here is to provide

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an individualized learning experience. So
based on that diagnostic, students are

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only given the modules they have
potential gaps that were identified by

00:15:19.149 --> 00:15:24.040
the diagnostic. So this lets your
stronger students go through the app

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faster and it also gives that extra
additional support to those students who

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are being identified by the diagnostic
as having those potential gaps.

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Additionally the modules give the
ability for differentiated learning. They

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can be assigned apart from the
diagnostic by teachers for homework or

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they can be assigned in conjunction with
the diagnostic as well as the summative.

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And this is something we're gonna look
at some of the features later on of how

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to do this but it works very very well
in the classroom.

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Following the targeted upgrading modules, the students unlock

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the summative assessment which would
assess the level of mastery achieved

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from the diagnostic. The summative does
follow all the same assessment framework

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and the idea here is just to cover the
exact same performance expectations and

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ensure that the student is improving. The
items are drawn from the same banks of

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questions ensuring that they are
consistent and valid.

00:16:34.709 --> 00:16:39.160
However they are variants of the
diagnostic so the assessments are still

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unique for each and every test taker. Now
I'm going to quickly show you guys what

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these lessons look like. The upgrading
modules are the part that gets students

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really excited about this tool. So here
from inside the app, this is what a

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lesson would look like following the
diagnostic on decimals. The student would

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Eric, Julie, and Janet's mom gave them 100 dollars for doing the gardening.

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They have to split the money evenly which
means they need to divide 100

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dollars into three equal parts. They start
splitting the money. First,

00:17:19.120 --> 00:17:28.780
they each take 33 dollars. They are left
with one dollar. They split the dollar and each gets 33

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cents. 1 cent remains. Now what? How can they split a cent into equal parts?

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This is not
possible since there is nothing with a

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value of less than one cent. So in
talking about money, we always round the

00:17:42.460 --> 00:17:48.370
final amount to two decimal places.
Sometimes we need to round numbers to

00:17:48.370 --> 00:17:55.480
more than just two decimal places. This
is Janet. She is a stockbroker for a large financial company. Today she is overseeing

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the sales of shares of BIG hamburgers - a
global fast food chain of restaurants.

00:18:01.059 --> 00:18:05.970
The price of each individual share is 3.5045 dollars.

00:18:05.970 --> 00:18:14.679
A client wants to buy 10 million shares of BIG. Janet calculates the total cost of the

00:18:14.679 --> 00:18:19.000
purchase. 10 million multiplied by 3.5045 dollars

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which comes to 35, 045, 000 dollars. Let's see what happens if Janet

00:18:28.059 --> 00:18:32.470
rounds the share price to 2 decimal
places instead of 4. The share price

00:18:32.470 --> 00:18:38.350
becomes $3.50. The total cost for the
purchase becomes 10 million multiplied

00:18:38.350 --> 00:18:44.020
by $3.50
which comes to 35 million dollars.

00:18:44.020 --> 00:18:48.789
The difference between the total using the
real share price and the total using the

00:18:48.789 --> 00:18:54.880
rounded share price is $45,000. Had Janet
rounded the share price to 2 decimal

00:18:54.880 --> 00:19:01.990
places when calculating the total, she would have lost her company a lot of money. Here we

00:19:01.990 --> 00:19:06.909
have a set of decimal numbers. Round
these decimals to whole numbers by rounding to the

00:19:06.909 --> 00:19:15.309
ones place value. So as we can see here,
the way these upgrading modules work is

00:19:15.309 --> 00:19:20.610
they introduce the concept and that
question of so what and why in numeracy

00:19:20.610 --> 00:19:26.740
before moving on to these interactive
components. Now again these are not just

00:19:26.740 --> 00:19:30.820
static videos. They do have these
interactions where the student has to

00:19:30.820 --> 00:19:39.159
engage with the system. I'm just gonna
get a few things wrong here. Don't judge

00:19:39.159 --> 00:19:43.710
me but I'm just showing you what the
system does. So here's an example of

00:19:43.710 --> 00:19:50.890
embedded feedback for the student and
they get another opportunity to complete

00:19:50.890 --> 00:19:55.830
the activity successfully. Now the idea
behind here is to work them through

00:19:55.830 --> 00:20:01.179
multiply sorry progressively harder
and harder tasks with those micro steps

00:20:01.179 --> 00:20:06.280
building up the larger concept of
numeracy. Another thing I want to point

00:20:06.280 --> 00:20:09.087
out is the the tracking and captions at the bottom.

00:20:09.087 --> 00:20:11.679
Rounding is often required to communicate the

00:20:11.679 --> 00:20:16.000
result of financial calculations because
many of them result in a large number of

00:20:16.000 --> 00:20:25.090
decimals when often all we need is two
decimal places at the most. Round the

00:20:25.090 --> 00:20:29.580
following numbers to two decimal places.

00:20:29.850 --> 00:20:36.450
So again here is another component where
the system is testing the student.

00:20:36.450 --> 00:20:40.680
On the bottom here there is a counter. There is a pre-built based on that diagnostic

00:20:40.680 --> 00:20:56.150
how many successive answers I need to
get correctly before moving on.

00:20:56.150 --> 00:21:04.400
I got one wrong so the counter will reset.

00:21:20.400 --> 00:21:22.900
Now that I have successfully completed five attempts I can move to

00:21:22.900 --> 00:21:29.410
the next segment. This is essentially how
most of the lessons work. I'm not going

00:21:29.410 --> 00:21:34.060
to go through all of them but I hope
that you do sign up for a demo to have

00:21:34.060 --> 00:21:39.640
access to these rich embedded voice
enabled upgrading modules. You can

00:21:39.640 --> 00:21:48.790
explore them as the teacher without
completing the diagnostic. Here we have

00:21:48.790 --> 00:21:55.870
an example of the teacher dashboard of
the app. You can see here that you have

00:21:55.870 --> 00:21:59.890
your students first name and last name.
Obviously this is not real data. And it

00:21:59.890 --> 00:22:04.210
gives you that quick snapshot of
performance of your individual students

00:22:04.210 --> 00:22:11.400
in each of the nine topic areas. Their
diagnostics and their upgrading progress.

00:22:11.400 --> 00:22:16.330
From here you you also have the option
to download the student reports in the

00:22:16.330 --> 00:22:21.400
third column from the right. This will
provide an individual report for each

00:22:21.400 --> 00:22:27.310
student on those 9 foundational topic
areas and you can also add students on

00:22:27.310 --> 00:22:35.320
the bottom. Let's take a look at some of
the more in-depth features a

00:22:35.320 --> 00:22:43.780
teacher can also see when looking at
students. After selecting an individual

00:22:43.780 --> 00:22:48.580
student name from your list, you have the
option to download a student learning

00:22:48.580 --> 00:22:55.030
report. This will generate a PDF with a
summation of the progress across that

00:22:55.030 --> 00:23:00.760
moment in time throughout the app. It will
show you the time spent on the app as

00:23:00.760 --> 00:23:05.920
well as the number of assessments
completed and progress through those

00:23:05.920 --> 00:23:10.660
nine foundational areas. These are
sometimes used for reports to academic

00:23:10.660 --> 00:23:17.290
advising, parents of the students, or even
the students themselves. In addition to

00:23:17.290 --> 00:23:22.540
this holistic learning report, you also
have the ability to download the

00:23:22.540 --> 00:23:28.450
individual assessment reports. Here you
can see the expected response alongside

00:23:28.450 --> 00:23:33.740
the submitted response.
These are available for both the

00:23:33.740 --> 00:23:42.860
diagnostics as well as the summative on
a student by student basis. Teachers also

00:23:42.860 --> 00:23:49.610
have access to an agenda which lets them
assign specific modules or formative

00:23:49.610 --> 00:23:54.860
assessments for their students in class.
They can select the open date as well as

00:23:54.860 --> 00:24:01.430
the close date as seen here for a number
sense from Monday, September 9th to the

00:24:01.430 --> 00:24:07.640
16th just as an example. And you can set
multiple agendas for individual students

00:24:07.640 --> 00:24:12.170
or multiple classes based on the
diagnostic performance of each and every

00:24:12.170 --> 00:24:21.680
student. There's several different ways
that the app can be accessed. Of course

00:24:21.680 --> 00:24:27.260
it was initially designed to be an iOS
app. So it is on the App Store. Simply

00:24:27.260 --> 00:24:31.610
type in the OCMT High School Edition
and it can be downloaded on any iOS

00:24:31.610 --> 00:24:38.270
device. It's also accessible through a
browser on the laptop or desktop or even

00:24:38.270 --> 00:24:45.560
a Chromebook. Simply go to mathematic
without vowels - that's mthmtc.vretta.com/ocmt

00:24:45.560 --> 00:24:53.180
and either sign up or enter
your login credentials. Again I just want

00:24:53.180 --> 00:24:59.000
to quickly mention, it was initially
designed for iPads. It is now fully

00:24:59.000 --> 00:25:03.890
mobile compatible as well which does
give it a better extension beyond the

00:25:03.890 --> 00:25:08.540
classroom. I have first-hand experience
watching a student complete a diagnostic

00:25:08.540 --> 00:25:12.500
in a class after the teacher introduced
the app and following the end of the

00:25:12.500 --> 00:25:17.180
period, I saw students pick up their
phones right away, in between you know

00:25:17.180 --> 00:25:21.830
one class to the next, complete their
upgrading modules, which was really cool

00:25:21.830 --> 00:25:29.210
to see and impactful. After downloading
the app or accessing it through a web

00:25:29.210 --> 00:25:32.900
browser, students can simply create their
new account,

00:25:32.900 --> 00:25:39.260
enter their class code, their name, select
their own username and password, and join

00:25:39.260 --> 00:25:43.390
the class. It's that simple.

00:25:48.230 --> 00:25:53.130
When students are active within the
class, if they have no immediate

00:25:53.130 --> 00:25:59.370
assignments from an agenda or their
teacher, they are able to select modules

00:25:59.370 --> 00:26:05.760
from the left, and begin selecting their
individual diagnostics. Now if they

00:26:05.760 --> 00:26:12.529
access this from a mobile device, they
will land on those nine topic areas and

00:26:12.529 --> 00:26:17.580
they can select the individual
diagnostics from that way if they don't

00:26:17.580 --> 00:26:24.090
have an assignment or are prompted for a
specific assessment. Once they complete a

00:26:24.090 --> 00:26:29.370
diagnostic, it will open up this sort of
timeline that you see here in the second

00:26:29.370 --> 00:26:34.139
window, directing them to the individual
modules they need to move through

00:26:34.139 --> 00:26:39.690
completion based on their score, you know
some students will have more or less

00:26:39.690 --> 00:26:47.519
modules to complete. After completing the
diagnostic assessment, students will be

00:26:47.519 --> 00:26:52.380
given access to only the modules they
need to complete based on that

00:26:52.380 --> 00:26:58.500
diagnostic. On the bottom here you can
see an example where the student tested

00:26:58.500 --> 00:27:04.019
out of the place value module, however
they have to complete reading and

00:27:04.019 --> 00:27:07.950
writing numbers, as well as rounding
before unlocking these summative

00:27:07.950 --> 00:27:13.409
assessment. These modules are what I
demoed earlier. They're rich interactive

00:27:13.409 --> 00:27:19.440
and voice-enabled and the goal here is
to go through those mathematical

00:27:19.440 --> 00:27:28.760
concepts and really work their way to
mastery. So that concludes

00:27:28.760 --> 00:27:35.330
tour of the OCMT app for secondary
students. I'm now going to pass off to

00:27:35.330 --> 00:27:41.090
Emily Brown to talk about the results
and analysis of the data that came from

00:27:41.090 --> 00:27:44.100
that research project.

00:27:44.100 --> 00:27:53.480
Thanks James. When
we look at student performance across

00:27:53.480 --> 00:28:00.380
the nine modules in the framework, we
see a steady increase generally when

00:28:00.380 --> 00:28:04.790
between when students took the
diagnostic assessment and then completed

00:28:04.790 --> 00:28:09.650
the remediation modules to how they
achieved in the summative assessment.

00:28:09.650 --> 00:28:16.270
You can see a steady increase in all of the
modules except for a slight slight less

00:28:16.270 --> 00:28:21.100
achievement across the fractions module.

00:28:23.200 --> 00:28:27.920
Here we took the aggregate data of
students and looked at their final

00:28:27.920 --> 00:28:34.430
grades in their grade 9 applied math
course as well as their EQAO scores from

00:28:34.430 --> 00:28:38.840
that year, and we can see that those
students who completed all of the

00:28:38.840 --> 00:28:44.690
remediation modules did far better and
had far better grades in the course than

00:28:44.690 --> 00:28:49.940
those students who completed some of the
recommended modules, and again compared

00:28:49.940 --> 00:28:56.360
compared to the students who completed none, who
achieved a average final grade of 55.8%

00:28:56.360 --> 00:29:05.930
and a far lower
EQAO score. Here we compare the trends

00:29:05.930 --> 00:29:12.440
that were occurring with the EQAO scores
for grade 9 applied math where there was

00:29:12.440 --> 00:29:21.170
a steady and consistent decline until
the OCMT remediation was implemented

00:29:21.170 --> 00:29:25.820
and that year and following we're at
least seeing a change in the trend in

00:29:25.820 --> 00:29:30.220
the trend with some steady increases.

00:29:33.700 --> 00:29:41.419
So thank you very much for attending
this virtual presentation. For access to

00:29:41.419 --> 00:29:47.750
this OCMT app, please email at the email
address provided here and for any

00:29:47.750 --> 00:29:54.702
questions or further information, you can
contact me and James.

00:29:54.702 --> 00:29:57.350
Thank you so much Emily.

00:29:57.350 --> 00:30:02.890
Thank you James. Thanks everyone.
Take care.

