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1) The Learning Continuum

2) Differentiated Instruction 

3) Probability PLC 

4) Inquiry Based Learning 

5) Mathematical/Numerical Literacy 

1) The Learning Continuum

2) Differentiated Instruction 

3) Inquiry Based Learning 

4) Probability PLC 

5) Mathematical/Numerical Literacy 

My thinking about learning continuums has been developing over the second half of the 

course. I started thinking about transitional understanding and learning continuums when 

were discussing differentiated instruction. I started to consider who a student’s personal 

background and understanding from all past personal and developmental learning and 

how these factors impact the current learning, near future and post-secondary 

opportunities. 

Most recently while working on chapter 8 and 9 I have been thinking about how students 

thoughts developed from 2D shapes to 3D shapes to using formulas to calculate area, 

perimeter, volume and surface area and eventually to being able to graph and find the 

equation of a line and altitude of a geometric solid on a Cartesian plane. All of these 

progressions happen in different grades and each requires some level of prior knowledge 

linked between what has been and what is happening next. As a teacher understanding 

the relationship we have between content and as a link in a continuum makes me more 

aware of the role I play in the immediate. The goal is to work to distil down the critical 

content understanding through diagnostic assessment, then to package in a concise and 

consistent message new learning assess it through formative testing then to encourage 

students to decode and think critically about new learning and build their confidence to 

the point where they can remember more and do the whole thing all over again next year 

at a more advanced level of reasoning.

• Learning does not happen in isolation 

we are part of learning communities 

that encourage students to build on 

prior knowledge and gain confidence and 

understanding.

•     A student’s confidence with 

their prior knowledge and schema does 

not only influence differentiated 

instruction it also influences the flow 

of transitional growth and 

understanding. 

•     In my classroom I always 

want to be aware of want my students 

have learned and the ultimate base 

knowledge for success in subsequent 

grades so I can design lessons and 

activities that encourage conversation 

and ultimately confidence.

•     Part of transitional knowledge 

is the EQAO testing. As much as 

people have mixed feelings on the 

purpose of standardized testing it is a 

baseline to ensure that students are at 

grade standard and can help to identify 

areas of needs potentially that require 

additional support.

No two people are alike, no two students will learn in exactly the same way. Based on my pre-

existing knowledge combined with new information for the course I have been able to re-evaluate 

how much differentiated instruction plays a role in my professional practices. Differentiated 

instruction is the convergence of three major factors coming together at the same time. 

1)     Readiness to Learn – This could include factors such as age/maturity appropriateness 

of a lesson, has the child eaten breakfast, are there other home or school factors that could 

influence learning. Any factors that take a child’s attention away from the classroom are things that 

should be considered when evaluating student readiness for a lesson. 

2)     Learner Profile – This is not isolated only to a student who is on an IEP, however it 

takes into account every student and past learning experiences. A learners profile could include 

connection to the subject, modality of learning (visual, auditory, movement), and ability to process 

verbal and non-verbal communication. These factors include anything that is known about the 

learner’s educational history and learning strategies that will influence how information is received 

and processed. 

3)     Interest (Attitude) – I think this is the most significant factor because even students 

who face tremendous challenges are able to learn if they are motivated and see the purpose of the 

skill. A student’s attitude will either allow them to open themselves up or cause them to close 

themselves off the idea of learning more and building on what they know.   Interest includes any 

factors that deal with perception and overall willingness to participate and contribute. 

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•     By being aware of 

differentiated instructional factors 

lessons can be made that are more 

geared towards the needs, attitudes, 

abilities and general mentality of the 

classroom.

•     Knowing the differentiated 

profile of a student only indicates a 

snap shot of where a child is at this 

moment. This profile is dynamic and 

continues to change as the student 

learns, develops and build 

understanding. 

•     Each student in the classroom 

has a different profile with different 

strengths and different needs. 

Differentiating instruction can happen 

on both a classroom and on an 

individual student level. 

CLASSROOM CONNECTION

Starting early in the course we discussed the JUMP math program and the inclusion of inquiry 

based instruction and evidence based learning in math. Through this activity I found my thinking 

to be stretched because i could see the absolute value of inquiry based learning however i could 

also see what could happen if the lessons were not taught with intention and thought it could 

create confusion and anxiety in the students. 

In addition to thinking about inquiry based learning i was also able to evaluate the role that 

higher order thinking skills such as synthesis and evaluation played in the math classroom. I could 

see how students were able to gain confidence in their understanding and create strong and 

meaningful connections by allowing students to participate fully and connect mathematically 

using a more authentic modality of learning. I was challenged and motivated by reading about 

and evaluated the role that lower order thinking skills also played in a classroom. My synthesis 

began to shift as a result of new information and discussion. I started to pose questions to 

professional colleagues and course mates on how to balance diverse needs of learners, and see if 

a teacher could effectively teach a class while at the same time differentiate instruction enough 

to balance the needs of students who would learn as a result of different levels of Bloom's 

taxonomy. This is an ongoing challenge and one that I will continue to discuss when we get to 

the Differentiated Instruction portion of my portfolio.

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