DA with Derivatives

Math 31 Derivative Assessment

Complete a newspaper, newsletter, pamphlet, or any informational item showing how Calculus can be used in real life applications.

Your product must demonstrate your knowledge of:

·         Use of the product rule by taking the derivative of the product of two functions, both which have a minimum of 2 terms and are at least degree 2.

·         Use of the quotient rule by taking the derivative of a quotient of two functions, both which have a minimum of 2 terms and are at least degree 2.

·         Implementing the chain rule while taking the derivative.

·         Taking the derivative of a function which must use the combination of two or more of the following:

o   Chain Rule

o   Product Rule

o   Quotient Rule

·         Taking the derivative of a function which requires implicit differentiation. 

In addition, you must also:

·         Determine the slope at a point of a function.

·         Determine the equation of a tangent line of a function at a point.

·         Determine the second derivative of a function.

The work, determining the derivative and other answers can be supplied separate to your final product, but the solutions MUST make sense in the story, or scenario, you have placed them in.

Examples:

Recently the police has determined the crime rate of Red Deer can be shown by the function, c(d) = d^2, where c(d) is the amount of crimes committed on a day, and d is the day of the year.  This function applies to only the first 5 days of the year, then the function changes.  The rate of change of crime from day to day can then be demonstrated by the function c'(d)=2d, and the exact rate of change on the 3^rd day is 6 more crimes each day.

Sylvan lake was under attack, last night, by a mob equipped with catapults.  The height of one of the arms of a catapult, in meters, could be represented by the function h(t) = -t^2+9, where t is from 3 seconds before the arm reaches its maximum height to 3 seconds after it reaches it maximum height.  If the catapult launches its projectile at t = -2, the slope of the projectile would be 4 m/s and an acceleration of    -2 m/s^2 with an equation of 5(x+1)=y-5

What we can learn from a single donkey

Whether you believe in God or not, there is something we can learn from a single donkey Jesus rode on into the town of Jerusalem.  When Jesus was riding into Jerusalem, people were waiting in angst and delight to meet Him and maybe become a recipient of one of His miracles.  The donkey that Jesus rode did not receive on ounce of affection, respect, or even recognition for bringing this amazing man to their town.  Not one individual recognized the efforts, by the donkey, put forth to bring Jesus to this place but he still kept on.

As a teacher I sometimes forget why I am doing my job.  I lose focus that I am not here for recognition, affection or even respect from my students, but to teach them something they do not know.  I am not here because of the pay, the summer holidays, or even the access to free coffee every morning. This perks are great and I am thankful for them, but education should not be about me; it is about the students who enter my class daily. 

How many times do you do things because it makes your life easier, or it makes sense to you?  After reflecting on the donkey I have realized it is the students who should be in spotlight and not me.  My assignments, due dates, exams, quizzes, etc. should not be created to meet my needs but actually the needs of the students.  In the past I have forgotten this.  In previous years, I have created all multiple choice exams because they are easier to mark, I have set due dates around my schedule so I would have time to mark them, I have even taught concepts in ways that make it easier and quicker for me. 

Reflection sometimes hurts! 

I challenge you to change just one task into allowing the students having the full spotlight and you stepping back.  Whether it is allowing each student to set their own due date, each student deciding how they will be assessed, or even each student informing you how to teach, you could make a considerable about of difference in your classroom.

Always remember that our needs and wants are not always in the best interest of student learning, and that sometimes we need to be an ass. Donkey reference there ;)

What a DA clasroom looks like

I have written about how I am changing the definition of test to allow for differentiated assessment in my class.  Some questions arose so here are the answers.

My current class sizes are in the low 30s, some classes I have done this with in previous years were in the low 40s while others in the 20s. With the right amount of planning, I believe this could be implemented with any class which has a reasonable amount of students. As for prep time, out of 8 courses throughout the entire year I teach 7 classes. 

How does it look?

First, if you walked into my classroom you would see some students working in groups, others alone, and others receiving one-on-one assistance from me.  Some students would be working on a laptop, some on paper and pen, and others researching on an I-Pad.  I encourage students to assist each other, collaborate on problems and research how the math we are using relates to their own life. 

I give students the whole “exam” at once and don’t set a deadline, nor do I ask students to work on it alone.  The directions are to work on the “exam” during class time, create your own problems and solutions, work on it in any order you would like, and to hand in the parts as you complete them.

Students are then given 1 or 2 classes (depending on the exam) to work on it.  As students complete a question, not the entire exam, I can start assessing it.  If I am not helping a student I will assess the question with the student explaining their reasoning and solution. This keeps my time spent on assessment low as not all students are handing in the entire exam on the exact same day.  This allows me to spend more time critically analyzing each student’s work.

Now here is the key:

I don’t grade it!

I either give them verbal feedback, or if I am assessing it outside of school, I will provide them with written feedback and comments.  Students then have the option of correcting their mistakes and re-handing it in.  This process continues to either the question is completed at 100% or the student chooses to take the mark I would assign as a regular exam.  This is how I have turned my assessments of learning to assessments of, as, and for learning.  I also have redefined the idea of 100% in my class.

What if a student does not like the project?

Easy answer, a traditional exam consisting of multiple choice, numerical response and written response is always an option.  However, only a rare few of students choose this option.  Keep in mind this is not a threat or a way to motivate students to complete the project but just another choice a student has as to how they are assessed.

What if a student does not complete the project in the time set?

I do not give them a zero, give them late marks, or use any kind of grading consequence but require them to start coming in during lunch, or anytime outside of class to complete it.  The first meeting starts with a simple question, “Why isn’t it done?” 

Some reasons are heavy workloads in other courses or outside school responsibilities and then I give the student as long as it takes to complete the project, with him/her still coming in during lunch.

Another reason I often hear is that they do not understand the material.  This solution has me re-teaching the material and still requiring them to complete an assessment on the outcome.

All other reasons are dealt case by case.

I realized, with a traditional test, if students do not understand the material we give them a failing grade and move on.  In the past, I have tried to have students complete their mistakes, but once I have shown them their mark all motivation to learn the intended outcome has vanished.  This is the reasoning behind the no grade on their product until it is complete. 

Students are enjoying this way of assessment as it gives them choice, autonomy in the way they can demonstrate their learning, and allows for authentic learning to occur.  If I have not answered a specific question, or you still have concerns, please let me know.

Differentiating Assessment for Different Types of Learners and Levels

Amber Henrey, whose site can be found here, is implementing a strategy to combine standardized tests in conjuction with differentiated assessment.

Differentiating Assessment for Different Types of Learners and Levels:
How one school successfully uses standardized tests in conjunction with differentiated assessments.
By Amber Henrey
September 14, 2011

Every year teachers are faced with the same dilemma: giving students the (almost) end of the year State Test. It is a standardized test, meaning it is given to all students state wide during the same time frame, in the same exact way, with the same exact questions.

The problems is that not all students were taught or learn in the same manner. As a data-manager as well as teacher for my school this problem haunted my grade level and me as we tried to sleep at night.  We know that out of our 90 students we have huge discrepancies in everything. Socioeconomic status gap was far and wide. English language levels were diverse. Simply the matter of sitting still for a length of time varied between students. There was no way we could effectively teach such a diverse population without addressing the diversity within our classrooms.

We decided to switch for core subject matters from heterogeneous homerooms to homogeneous core classes. Every teacher still taught all the subjects but our kids went between us at different times of the day. It used to be called tracking but I will explain why it isn’t.

To start the year off the students are grouped by a combination of CST scores and teacher recommendations to get the core classes going. 4th grade is the first year these kids are grouped homogeneously so one teacher’s advanced student may be another’s proficient. We monitor who is standing out in the group and adjust accordingly.

During the first month of school we give dreaded assessments. Its not fun but it must be done so that we can quickly diagnose learning abilities and missing skills . We try to keep it to 30 minutes once or twice a day. The assessments are diagnostic and formative in nature. This helps us monitor gains made during the year but also helps to determine our Targeted instruction. The whole grade level takes a mock CST for 4th grade standards to help us make more decisions about who to teach and what to teach them.

Once the results are in we adjust the three groups for Language Arts and Math. If we could have 5 groups it would be ideal but we only have three fourth grade teachers. The advanced to high proficient group maxes out at 35 students specifically assigned to the teacher that has GATE credentials, and is truly an expert at teaching students to utilize their higher level thinking skills. The high basic to proficient group also maxes out at 35 students. The basic to below group hovers around 20 students unless they are pulled out for resource at this time.

The groups are taught the same skills and essential standards at the same time but in different ways. You may see different levels of text and pacing however you will see that if comparing and contrasting is occurring in the advanced class it is occurring in the below basic class as well.

We give weekly assessments based on that specific skill. We do not give “story tests” because we aren’t teaching story recall. We find an alternate text for the kids to read. We select passages that match our theme or genre. We create questions using question stems for our focus and using blooms taxonomy.

Here is where the differentiation comes in. If a student’s reading level is high they take the assessment at their reading level. The questions are the same questions given in the lower levels however they tend to be more open ended. The expectation is that they will be able to answer the question without any other prompting. The middle group has a text at their level but the questions typically have a sentence starter or frame for them to fill in. The lowest level has reading at their level. Their questions are typically fill in the blank with an example or vocabulary list. If necessary we use a multiple choice format as well. We try to mix the types of questions on each test so that we can see if the kids are able to do the standard or are just good at test taking.

Here is what is key:
We focus on the skill and standard chosen as a grade level for that week. We create tests that assess the skill and standard, not if they can do everything at once: read a certain level, write, or spell.  If a group can do all those things and demonstrate mastery of the skill then they are assessed in a way that has all the components.. If they cannot do all those things then they are given an assessment in the manner that they can. Regardless of how they show it; if they can demonstrate that they can accomplish the skill or standard then they are considered a success.

Back to the issue of tracking. Our kids do not stay in the same groups all year. We have flexible groupings. If a student has demonstrated mastery for 3 or more weeks they are often switched into the higher group. The reverse also happens. If a student is not able to keep up with the rigor of the class they are in than they can be moved into the lower group.  There was a time where almost an entire class has changes because one teacher was really able to teach something well while another wasn’t.


We also address the fact that kids have gaps to fill or enrichment to extend. We have another block of instruction called Target Time. We have additional support staff that help us break our groups into even smaller specific groups for 40 minutes 4 days a week. These kids are grouped based on their diagnostic assessments and given time to work on their gaps and one specific standard at a time.  A pre-assessment is given every three weeks for that one standard and one skill the students are working on. Then at the end of the three weeks a post assessment is given. These assessments directly relate to the groups ability. Groups are rearranged as needed.

The students know what group they are in and why. We know kids notice that they are homogenously grouped and instead of acting like it isn’t so we are up front about why they are placed where they are. “This group was created because on the assessment we gave on making predictions using context clues you scored less than 75% we are going to focus directly on that standard for the next 3 weeks and give you an opportunity to move groups again.

This is the third year working this way and so far we haven’t had any issues of insecurity or teasing. If anything it is a relief for our students to be with common peers struggling with similar issues or ready to be challenged. Our CST test scores took a grade level from 39% proficient in third grade to 64% proficient in fourth grade. We continually evolve our procedures and streamline them.

DA with first principles and limits

Here is an example of how I have changed the definition of an exam.  Before, when assessing first principles and limits in my calculus class, I would have each student write an exam.  This year, I am giving students the option of writing an exam or completing the following to demonstrate their learning.

Unit 1 Assessment Project

1.      Create a formula for the distance of an object at any time t.  The formula must be at least degree 2 with a minimum of 2 terms.  Using your formula you must:

·         Determine average velocity of the object for the first 10 seconds.

·         Determine, with an explanation, the instantaneous velocity after 10 seconds.

·         Determine, with an explanation, the instantaneous velocity for any time t.

·         Determine if the object is ever traveling 50 m/s.

2.      Create a piecewise function over the domain of the real numbers. The function must contain at least 3 different pieces and may not be continuous and may not have a limit at at least one point.  Using your function you must:

·         Provide a graph of your function.

·         Explain why your function is not continuous at the specific point.

·         Explain why a limit does not exist at the point above. Explain how you could change your function such that there is a limit.  Calculate the left and right side limits at this point.

3.      Demonstrate, through a real life application, how you can calculate the instantaneous rate of change at a specific data point.  You may use data from a chart, create a video, etc., but the data may not follow a specific function.  The point at which you calculate the rate is entirely up to you, but must have an explanation.

4.      Create three functions, one which:

·          approaches infinite,

·         one which approaches 0,

·         and another which approaches a line which is not 0

as you extend these functions to infinite.  Explain how you can determine the limit as x approaches infinite, for each of your functions.

5.      Create a real life example of a convergent series, and calculate the sum of this series.

Proof that DA works

As my last post with "Problems with Common Assessment" there is another side of the coin; "Differentiated Assessment"

Some are skeptical that there is a benefit in having DA in your classroom, but Bayview Glen School from Ontario shows there truly is.

Bayview Glen school is a K – 12 school that wanted to answer the question “How, as leaders, can we facilitate a successful shift towards differentiated assessment throughout all grade levels?”  The focus was to encourage teachers with the knowledge to expand their assessment policies beyond traditional tasks such as tests and quizzes. 

This school completed an action research plan by providing the entire staff, in June 2009, with an assessment workshop.  During this workshop, each teacher was educated on various Differentiated Assessment Tasks (DAT) which they would implement in the 2009 – 2010 academic year.  Then given a simple task:

create one differentiated summative assessment for their course and present this task to the staff, reporting on the assessment and providing insight into how it impacted student learning.

Immediately, the staff demonstrated a strong commitment and their assessments which were presented were creative, engaging, challenging and incorporated reflective elements of a constructivist approach to teaching and learning. 

After each teacher implemented their assessment in their own classes, they were to report their experiences with the rest of the staff.  What was noticed?

“The results of these assessments lead to greater student learning experiences allowing for meaningful connections to the real world.  We also realized that is wasn’t just about the culminating differentiated assessment task, rather we needed to emphasize the importance of formative assessment, digging deeper into our curriculum while placing students at the center of their learning.”

Some teachers reported:

“I am definitely trying to move away from the traditional way of instructing and assessing.  By being introduced to DAT, and by taking the first two terms to incorporate the ideas into my classroom, I have realized the possibilities and I am excited to continue to develop the use in my daily teaching practices”

One student even reported.

“The assignment for Glass Menagerie helped me to realize the relevance of this books’ message and how the themes applied to my own life, allowing me to provide a better analysis, while demonstrating my inquiry skills.”

In the school there was a shift towards student-centered learning, with an emphasis on making real world connections.  Inquiry-based learning activities allowed for a sense of wonder and curiosity amongst learners.

Before completing this action research all teachers completed a survey (named Survey 1) and after they completed the same survey (named Survey 2).  Here is how this one task changed their ideologies:

You can notice that teachers were changing the “bulk of their summative” assessment strategies after a single DAT.

Similar data is becoming more and more prevalent and should not be ignored.  Peter W. Cookson Jr stated:

“We are at a threshold of a worldwide revolution in learning.  Just as the Berlin Wall fell in 1989, the wall of conventional schooling is collapsing before our eyes.”

Problems with common assessment

I would like to challenge the idea of common assessment.  Not just common throughout a department but common even in a single classroom.  From this time further I will refer to these assessments as their true name “Standardized Assessments”.  The definition of a standardized assessment is:

a test that is administered and scored in a consistent, or "standard", manner. Standardized tests are designed in such a way that the questions, conditions for administering, scoring procedures, and interpretations are consistent.

 
I have asked why do teachers give common assessment?  I will provide the two top reasons I heard, and then my counter-argument.

1) Standardized assessment allows for fair and equal assessment practices between the same courses throughout the school.

Counter: What is fair is not always equal and what is equal isn’t always fair.  If we truly want equal assessment, then should we not require all students to write with the same hand, take off their glasses, set the temperature in all the rooms to be the same, and have all students write with the same type of pencil?  I know this sounds absurd, but where does the fair and equal practice stop?  Each and every student, in my class, has a different set of needs and abilities yet these exams will force each student to be put through the same hole.  Alberta Education recently, wrote

Differentiated assessment means selecting tools and strategies to provide each student with the best opportunity to demonstrate his or her learning. As you get to know your students, and as student differences emerge, assessment naturally becomes more differentiated, because its purpose is to meet students where they are and to coach them to the next step. In this way, assessment and instruction continue to support and inform each other.

By making these decisions before ever “knowing my students” how is one to decide which would be the “best opportunity for each student to demonstrate his or her learning”?  I do not see standardized assessment as a fair and equal practice at all.

2) Standardized assessment allows for fair and equal instructional practices between courses throughout the school.

Counter: This seems like the standardized assessment is more assessing the teacher than the student now.  Even if two students, in two different classes, receive the same mark this does not guarantee the same instruction has been given.  One teacher could be “teaching to the test” and involving daily test prep activities while the other is implementing quality instruction and critical thinking.

Now, the problems I see with common assessment:

First and foremost: It is the duty and responsibility of the classroom teacher to determine how and when to assess each student.  I am confused and distraught when people, outside the class, control the assessment strategies, without even knowing the individual students they are impacting.  

Alberta Education’s ideas are:

Differentiating assessment involves rethinking the standard practice of having all students do the same assessment tasks at the same time, regardless of their individual learning needs or the learning they have already demonstrated. Rather, in this new paradigm, teachers customize the selection and use of assessment information to reflect each student’s highest level of achievement.

Also, I refer to these as standardized assessments as they are designed in such a way the class average should fall in a “reasonable” zone.  This zone may differ from teacher to teacher and from class to class but this underlying bell curve does exist.  I have heard of meetings where discussions such as “The average was low, so the test should be made easier” or “The average was too high, so we need to increase the difficulty” have been had.  This saddens me as we are requiring students to fail such that others can feel success.

Since by the definition and the manner these assessments are designed, usually, they must fall on a specific day, common to all teachers of the same course, and also consist of some mixture of the following:

·         MC 5-10 questions
·         NR 3-5 questions
·         WR 2-5 questions with bullets

Usually the test days, and requirements are decided before the first day of school

By having standardized exams, we are going against the research and knowledge of our government.  Also, it should be the freedom of the teacher to decide, and indeed, the freedom of each student to decide how and when they will be assessed on their knowledge.  Of course we all know that some people employed as teachers are of different quality, but by forcing everyone to assess, and ultimately, teach the same way it may not improve teachers of a lower quality but actually hobble the good ones.

Assessment from Esme

I am very pleased and honoured to have Esme Comfort, whose blog can be found here, to share her ideas on Assessment with me.  Below is a guest post from a Public school Trustee in Bow Valley.

"Said the Source" by Micah Lexier, Library Installation, Hamilton, ON Photo: Wendy Bush, with permission

Pleased and proud that the teacher, @d_martin 05 (as he is known on Twitter), has asked me to do a guest post on his blog. He is a highly committed educator who is always honing his skills.

The topic? “What is the best way to gauge a student’s progress in learning?” Or [drum roll] ASSESSMENT

You may as well ask, like Lewis Carroll’s Mad Hatter, “Why is a raven like a writing desk?” because there is no one definitive answer. Rather it is a complex blend of sometimes competing interests that are served by student assessment; hence the choice of the photo above.

So what could this little old lady trustee have to offer to shine some light on the subject? First a disclaimer: I have no pedagogical credentials, just the experience of having been a student and having children who were/are students. Let’s start with some definitions and descriptions, per The Wikipedia of Esmé, i.e. my own best understanding, as a layperson.

•                    Formative assessment is an approach to teaching and learning with feedback as its mainstay, in a supportive classroom context. Assessment is ongoing and student-centred. Differentiated instruction, the teacher as a lifelong learner and professional learning communities – and more – will factor into this process. Parents trying to wrap their heads around this idea will often exhibit these first responses: “What d’ya mean ‘no homework’? No report cards – what the...?”

•                    Summative assessment is a measurement, at a specific point in time, of student learning relative to curriculum or course content. This is generally done by different sorts of tests, quizzes, set assignments with tight rubrics and so on. The Provincial Aptitude Tests and Diploma Exams are full-on examples. We are all very familiar with this “old school” methodology. Numerical marks or letter grades are usually awarded.

In my ideal world, summative assessment would only be used to inform formative assessment; PAT scores would not be published or shared, except between educators to use to inform their practice and diagnose trouble spots. Teaching and learning succeeds best, IMHO, when the teacher and the student are given respect and autonomy.

However, this is tricky stuff. Public schools are accountable to the children and parents, but also to the provincial government and the taxpayer. An easy way to determine if outcomes have been met is indeed the use of hard numbers and straightforward comparators. But what are the outcomes?

Should every student move to post-secondary education immediately after graduation? Well, all of life after high school graduation is post-secondary education, isn’t it? Hold it. Every student should graduate high school, right? At the same age and stage of life? We need to think which skills and attributes will best serve our students, will best prepare them for their individual futures. I believe those are much more difficult to – ahem – sum up. And much, much more difficult to teach.

For those of us who sat quietly at our desks, soaking up the wisdom dispersed by the pedant at the front of the room, the transformation of education will be hard to comprehend. Effective formative assessment means collaboration between teacher and pupil to adjust teaching and learning while they are happening. That was not my experience of school! That is why school district administrators and governors must involve the parents closely on this journey; it’s crucial to providing the support teachers need. Parents need to try to understand the process and work with the teachers to benefit the children.

When my first parent-teacher interview rolled around, some 20 years ago, I thought long and hard about how to use that precious 10 minutes. What did I want to know? At the time my two questions were:

•                    How is my child doing, relative to the teacher’s perception of his capacity?

•                    How is my child doing, relative to the progress of the other students in the class?

Now, it seems to me, I was really asking: “How well do you know my child?” That relationship is worth more to my child’s lifelong learning curve than the ability of the teacher to stuff facts/data into his head. Formative assessment means student and teacher are learning together, and the subject matter is always: the student. It demands more commitment, more rigour from both sides than a straight “drill and kill” testing regimen ever did. Successful students and successful teachers are “curious and curiouser” as a matter of course; the thirst for learning never is slaked.

Geometric Sequences Reductions

Here is an activity I created to introduce geometric sequences. 

1) Watch the movie below:

2) Determine the dimensions of the last image if the original image was 210 × 297 mm.


**I had a copy of the original and final image and had students measure the original on their own, and then check their answer by measuring the final image.**

3) Extenstions: If we combined all the images, determine the total area.

If I extended this sequence to infinite, what would be the limit of the sum of the sequence?

Intro to Tangents

Here is an activity I used in my Math Calculus class to introduce tangents at a point.

I gave each student a copy of the video below.

Then, in groups of 2, students had to answer the following questions (which is part of the comments in the full YouTube video)

1)  Watch the video

2)  Determine the average speed for the first 5 minutes.

3)  Determine the average speed for the entire trip.

4)  At the end of the video, the speed of the vehicle is 109  km/h, explain any discrepancies from your calculation in part 3.

5)  Determine the average speed of the vehicle after 15 min of driving.

6)  Determine, with the least amount of error, the speed of the vehicle  after 15 min of driving.

7)  Explain, if any, the difference from part 5 and part 6.

Feel free to use, change as you seem necessary.

For the parts that is hard to see:

The time at each break in the bottom right corner is the total driving time to that point.
The distances at each break are -7.6 km/16.7 km/23.3km/32.1km

I do apologize the video is quite horrible with YouTube.  The original is much better.  If you require a copy of the original, email me and I can get you a copy.

The product or the mark?

Over the weekend I tweeted “A great exam makes a teacher proud while a good project makes a student proud” and received some unpleasant responses.  Knowing this would take more than 140 characters, I wanted to elaborate on what I meant.

I am not denying that some students are proud when they receive a great mark on an exam, but I believe these students represent the minority of the group.  When I look around my classroom, I have posters, Parachutes, Enlargements, graphs, and other math projects which have all been created by students.   After looking through mine, and my colleagues’ classrooms, I have yet to find a unit exam posted on the wall.

Remembering back in my own schooling, I recall creating gumball machines, paper mache figures, and even a sundial I gave to my mother for Christmas, but yet I vaguely remember the 90+% mark I received on my  math 30 diploma.  Going through my scrapbook, I don’t have a single test or quiz among all the projects I kept.  Also, for most of these projects I don’t even have a clue as to the mark I received on them.

What does this mean?

I believe that most students are more proud of the product they create than the mark they receive on something the teacher created.  Last year, I had students wanting to show their parents their creations BEFORE I had even assessed it!   Has a student ever asked to show their parents their exam before you give them their mark?  

School should be giving each and every student a chance to feel success and accomplishment.  For some, I do believe this can be in the form of an exam, but for most this will require a different form of assessment.  Open-ended projects move beyond traditional assessments and, if made properly, require students to communicate their thinking in a deeper manner. 

I am not saying that high marks on exams should be discredited, or don’t represent that learning has taken place, but just suggesting that open-ended projects will allow for success for other students in the class.  Remember, differentiation should start with instruction but continue onto assessment.

Differentiated Assessment

I have had a great enlightening summer and would like to start things off with a bang!  Differentiated Instruction (DI) and Differentiated Assessment (DA).

Most teachers speak of DI as a common practice in their class and truly teach to the needs of EVERY student.  However, some teachers require these same students to jump through a common hoop of assessment.  This assessment can take forms of unit exam, a worksheet, a quiz, or any assignment which is the same for ALL. 

If we speak of DI so commonly, where is DA?

Rick Wormelli in Fair Isn't Always Equal: Assessing and Grading in the Differentiated Classroom states that "Assessment informs practice, and we take action".

DI MUST lead to DA in a classroom!  In a truly differentiated class, students can work towards learning outcomes at different paces, using different strategies, and mastering outcomes in different order.  As a result, teachers will need to assess these strategies differently and accommodate the assortment of learning styles while still measuring the learning outcomes.  Assessment and instruction does not have to be different but can occur simultaneously and appear different for each individual student. 

Alberta Education states, "The goal is not to have an individualized assessment plan for each student, but to have a manageable class assessment plan that is flexible enough to accommodate a range of student needs."

Some say assessment OF learning has to be common (or standardized).  Here are some examples of how we can have DA in assessment OF learning. (From Alberta Education)

Assessment of learning (sometimes called summative assessment) is the process of collecting and interpreting information to judge student achievement against predetermined criteria for the purposes of grading and reporting. Assessment of learning occurs at benchmark points in learning, such as the end of a unit or chunk

of learning. Consider the following examples of differentiating assessment of learning.

• Some students in a class choose to demonstrate their learning by writing a report, while others choose to create a poster, and still others choose an oral presentation.

• A teacher provides text-to-speech software and a digital version of the test to a student who has significant difficulty reading the questions in a social studies test.

• A teacher discards some marks collected early in the semester for a student

It can be done, and some our already doing it.  Assessment should not be a democratic process but an individual process.  Nor should assessment be done TO students, but actually WITH students.  Always remember you are not teaching statistics, data points, trends, or even groups, but actually living students with heartbeats, emotions, interests, and passions.