Saturday, October 11, 2014

Integrating My Way Through The High School Mathematics Curriculum!

I suppose this blog entry is not for everyone. Yet, it is time for me to write it.

It is about mathematics. Moreover it is about High School mathematics. More moreover, it is about a fundamental scope and sequence shift in the high school mathematics curriculum caused by the natural shift of state expectations for a college and career ready high school curriculum. Super moreover, it is about teaching an integrated high school college prep mathematics curriculum for all students!

If you are still interested at this point, then read on!  Otherwise you might just want to wait for the next blog!

AGA or IMP? 

It has been tradition in the United States, to teach the expected standards of the high school mathematics curriculum via courses named Algebra, Geometry and Advanced Algebra (or sometimes named Algebra 2). Often referenced as the AGA sequence of courses, there was an aura and perception that the AGA sequence of isolated topics resulted in a lack of rigor in student learning, with an inappropriate emphasis on low level procedural knowledge and fluency (or computational fluency and drill), using memorized
algorithms for finding a “Math” problem answer (cross multiply and divide anyone?)

During the 1990’s (and a bit before) there was a niche middle school U.S. market referenced as Integrated Mathematics that had a few in-roads into high school math curricula, but not significant or widespread implementation success nationally. These programs were perceived to be better at increasing student conceptual understanding, but were often criticized for deserting computational fluency.

AGA was criticized as a curriculum that was a mile wide and an inch deep, with not much application or understanding. Integrated mathematics was criticized as a curriculum that was too deep, based on nice “Math” problems with not much connection to student proficiency on actual standards.

Of course neither extreme painting of these two seemingly opposite course pathways for the high school standards was completely accurate. There were many successful AGA and Integrated programs, and there were of course many non-successful examples as well. In reality much of the “success” of these programs – from a student learning point of view  - were not so much about the scope and sequence of topics within the program per se, as much as it was about the teacher or teacher team using the program.

In pursuit of AND

I have always thought that either of these extremes was not best. Why couldn’t students benefit from a high school mathematics curriculum – a teaching and assessing program- that was both? Why not have fewer standards, taught at a deeper level of complex reasoning for student understanding, AND develop the essential procedural knowledge and skills needed to demonstrate student learning via the route of higher-level cognitive demand tasks (Thus redefining what is meant by mathematical fluency)?

This was the real gift to the high school mathematics standards offered up by the CCSSM. And the efforts made by states such as Texas and Virginia to intentionally blend conceptual understanding standards with procedural fluency standards AND allow the former to influence student learning of the latter via a set of mathematical practice and process standards.

The CCSSM Conceptual Categories of standards in high school created the potential for an integrated theme around:   
           
            Number and Quantity
            Algebra
            Functions
            Geometry
            Statistics and Probability
            With Modeling

These big idea categories and the 138 or so corresponding standards were not designed to be about any course per se. They were designed to help the reader understand the nature of the Coherence (Sense –making), Rigor (a balanced approach to understanding, procedural fluency, complexity of reasoning and applications) and Focus (Fewer standards).

 Just as Number and Quantity, Functions, and Modeling are not separate courses students take, neither should the Algebra standards, Geometry standards or Statistics standards be thought of as completely separate courses that isolate topics and standards within a given year.

We can call the courses students are to take in their first three years of high school mathematics whatever we want, but even if you chose to call it algebra – it has been forever changed for 2015 and beyond.

WHY?

First, we don't really write mathematics textbooks anymore. We write mathematics content for which the textbook is just one format. Students and teachers can access the content online, on their ipad, or iphone or other web-sourced/app device, and they can “experience” the content in a more dynamic way via video resources, games, and other forms of digital intervention and formative support.

Second, the modern day high school Algebra 1 course and all high school courses are now more integrated, regardless of the course title. The 1st, 2nd, and 3rd year of high school mathematics a college and career ready student learns is now built on a foundation of progressions and themes within each course and across the three courses.  So, which is better for high school students? An AGA sequence or an Integrated sequence? I am asked this question almost every week!

The answer is


It is not the names of the high school courses that ultimately will impact student learning. It is not whether you call a high school math course Algebra 1 or Mathematics I.  Geometry or Mathematics II. What matters above all else, are the quality, design and nature of your lessons and assessments every day.  

And yet, there are some great benefits to teaching these high school standards within a scope and sequence that takes advantage of expanded ways of student thinking, if the content progressions are to adhere to certain rhythms for student learning. These choices though are not dependent on the claim of AGA or IMP. These scope and sequence integrated shifts should occur no matter what you choose to call your courses as student learning experiences are based on a natural progression of topics. As one example, consider the role of:

Functions: Notice that in this more modern day view of the high school curriculum, students do not write a linear equation, rather they build a linear function, an exponential function, a quadratic function, a logarithmic function, etc… Building functions, interpreting functions, and analyzing functions are a major aspect of the high school curriculum now - generated from within and by a modeling context. This work, from a standards progression point of view should  be placed in advance of the equation solving aspect of the curriculum.

At the risk of getting just a bit specific in a blog entry, imagine a yearlong progression for the standard: I can build a function that models a relationship between two quantities.

This progression would begin with arithmetic sequences (constant rate of change) in Unit 2, move to linear functions (Unit 3) and then linear statistics (Unit 4), followed later by geometric sequences (constant percent rate of change) and more statistics in Unit 6, exponential functions (Unit 6 or 7) and eventually quadratic and polynomial functions  (Units 9 and 10). Thus, the standard has a logical progression for student learning built within the course – across multiple conceptual categories.

Equations:  A correct sequence to follow out of the building and interpreting of functions is to extend function development to include the topic of equations as the equivalence of two functions. This opens the door for students to solve linear, exponential, quadratic and other types of equations using three representations: Numerical (or table), visual (or graphical) and analytical (algebraic). What happens in your class, when students are asked to demonstrate fluency on a mathematical task such as:  

                                                Solve: x^2 + 2x = -3x -7 
 
If students have first experienced standards on how to build and interpret linear and quadratic functions, then multiple solution pathways become available or a lower level cognitive demand task such as this. In an AGA course sequence this standard would be taught in the spring of ninth grade. In an Integrated course sequence this standard would occur sometime in the fall of tenth grade, but the progression for building functions, then equations would still hold true. 

In this simple example, it is not about the course, as much as it is about your commitment to integrate student work with functions as a precursor to equation solving, and of course choosing a balance of higher and lower cognitive demand tasks in the process of building student fluency and understanding.

There are many more integrated topics and progression of standards to explore and discuss..., but not in this blog. However, one of the more elegant aspects of the geometry clusters is the use of transformations  (functions) as one of three ways to explore, justify and reason within the geometry standards. Thus, functions play a deeply embedded role throughout all three years of high school mathematics. 

For deeper insight I invite you examine our recently released high school mathematics series. We have also given the integrated question and series a lot of deep thought over the past 2.5 years as well.  We hope this will help you in your high school standard mapping journey - whatever integrated path you might choose! 


Wednesday, August 13, 2014

Embracing the Privilege of Another Season!

I met with all of the grades 6-12 mathematics teachers in Elk Grove Unified (CA) this morning, while on my way to Grand Rapids to meet up with some great folks in Michigan.

Opening day for the Elk Grove teachers is this Thursday. Another season is beginning. The kids are coming, ready or not! And then, in the blink of an eye, it will be May 2015 and this season will end. And I wondered what kind of season would it be for them?

I do not pretend to know these educators very well, really. This was my first opportunity to work with them. I know we love the same job – teaching kids math in grades 7-12. But at this stage that is all we have in common. And they do not know me either, anything I had to say would only make a difference if they chose to embrace the ideas I shared - every day, week, month and season.

 So, I gave them my best Mary Layco message I could give them.

The essences of my opening comments were as follows.

Our lives, our careers, revolve around one “season” after another. 2013-2014 just finished a few short months ago, and 2014- 2015 is about to start. A new season! Will it be a good one or not?

Then, 2015-2016 will be here before you know it, followed by the 2016-2017 season, and all of sudden here comes 2025-2026 and for some of you sitting in this room, that will be it. Your final season! No more chances to get it really right! Right?  

Only one problem, we don’t always get to name when our seasons will end. The greatest math teacher I ever knew, Mary Layco, died suddenly and unexpectedly last December and perhaps in one of the greater tragedies of this coming 2014-2015 season, she won’t be in it. She doesn’t get to open the season next week at Stevenson.  

She doesn’t get to name her final season. This teacher - who loved students beyond reason, does not get to open up a new season. And all who knew her suffer for it.

So, my challenge to the Elk Grove Unified teachers and to all of you who read this blog is simple. Are you willing to make this a great season, before it is too late? A great season for your students, and for you? Are you more than willing to be more like Mary?

Who is Mary Layco you wonder? 

When I got to Stevenson HSD 125 in Suburban Chicago in 1986 Mary was already on the staff, and I was her “boss” as the Director of Mathematics and Science. Mary was passionate about making every season of her teaching career really count. She believed in PMA - Positive Mental Attitude - and thought everyone of her colleagues and students should exhibit PMA every day. 

Of course in 1986 we did not have the research we have today, that informs us about how the choices Mary was making would result in great levels of student learning, but intuitively she knew.
In honor of Mary’s life, I offer three commitments necessary to ensure you will have a great 2014-2015 season. These worked for Mary, and they will for you too!

1. Eliminate The Use of Rows

Thanks to Mary, we destroyed the idea of students learning mathematics while sitting in rows and respectfully watching the teacher do mathematics. In 1994 we moved to a “teams of 4” model, and never looked backed. Mary was the architect of high levels of student peer communication. Twenty years later we have the highest performing students ever. And, Mary led the way for showing us how to manage that small group discourse effectively by engaging students in deep meaningful peer-to-peer discourse. In her soulful way Mary wanted to see and hear what her students understood during class.  

I do not know if the Elk Grove Teachers really believe if they can do this or not… but I hope they do. I hope that every one of them will work together to destroy the use of teaching in rows in their middle school and high school classroom structures.

2. Eliminate The Privacy of Scoring (Grading) Exams


 Score your Chapter or Unit exams (or some student samples from them) together. Mary was a master at creating and designing tests with her colleagues, and then double scoring those tests with them at the end of a unit as they calibrated their results and developed more accurate scoring of student work on those assessments. Those discussions often led to a more raucous debate about how to best teach concepts for deep understanding. Her unit-in and unit-out commitment to do this with her team, resulted in a much more accurate scoring of student work in our mathematics program.

3. Eliminate the Use of Lower-Level Cognitive Demand Math Tasks Only

Balance the rigor of your lessons with high and low cognitive demand tasks. If you worked on Mary’s team, you knew that you would be expected to “Up your game” and make sure that students had the benefit of developing deep understanding of the curriculum and standards for that course. She refused – refused to allow anyone on her team to make excuses for why kids could not learn. Mary’s mantra was not “How good do we have to be?” But rather, “How good can we be?” And she pushed everyone to rise up to that challenge. To reach for the sky of great results.


So, what will 2014-2015 be like for you? Will you have the courage to make this season of your life, of your career, really matter? Can you eliminate rows? Really? Go for it! Can you score/grade stuff together and ensure better accuracy to your grades you assign kids? Go for it? Why wait? Can you make sure you teach by raising your cognitive demand task expectations of what all kids can do? Go for it!

As I walked out of the session this morning at Elk Grove Unified, a veteran teacher and someone I suspect has worked hard for a long time to be more like Mary, stopped me to say thanks. His words did give me pause a bit though, as he said, “It was so great for you to be honest with us, and not give a “*!#” about our reaction – good or bad. Thank you for saying what we needed to hear.”

You know, I thought a lot about what he said when I got into my car. I sat there for just a few minutes with my quiet tears. The tears were for Mary. She doesn’t get to start on Thursday. The tears were for my own inability to deeply impact those that get the privilege of another season. I think too the tears were for the students who deserve for their teachers to have great seasons just like Mary, every year.

And, the tears were for knowing and understanding, just how hard that request is for any of us that call ourselves "teacher".

May you find your inner Mary and go for it in this season. Work together, learn from one another and give it everything you got. There really is nothing to lose – other than the privilege of that next season.
  

Sunday, July 20, 2014

Exercising my self-control muscle this summer!



July is one of those strange, yet beloved months for those of us in education. It is that month where we are no longer on a tight schedule controlled by the school calendar, the daily bell schedule, the controlled rhythm of the start and end of the school day, each and every day.

In July, we are between “seasons” so to speak.

It is our time for reflection, freedom from the daily routine, vacationing and recovering and so much more. No fixed routines! I love July!

We have chosen a work life that imposes a schedule upon us for 10-11 months of the year. If we do not exercise the self-control to follow that schedule day in and day out a lot of people in our school community are affected by our action (or inaction). And so, we adjust our lives to follow the routine of each and every day without reservation or question.

For many years, I so loved this routine. There was something in my hardwiring that needed the structure of every day, the movement of the bell schedule, and the consistency that followed one season after another. Lunch at 11:42AM every day. Perfect.

Then July would appear, and I could sleep in until 9:00AM, wear my jammies until noon, and maybe (get ready for this) not even shave until tomorrow! I could work out at 1:00pm, take a nap at 2:00pm and go to a movie during the week at 11:00pm! What freedom!

Only, after 10 months (or more) of tight daily schedules and a work rhythm I depended on to keep me under control, I really did not know how to manage that free time! How do other people do it I wondered? There are so many professions, so many jobs, where you can just break the routine, exercise your own self-control muscle and make your own decisions for how your work schedule today will be different tomorrow.

And then a few weeks ago, while drifting around the internet on a sunny Wednesday afternoon, I ran across an article from the Harvard Business review: “In the Afternoon, the Moral Slope Gets Slipperier” by Harvard professor Maryam Kouchaki.

Hmm, in the afternoon, I thought: “What about all of July?  In this Harvard Business Review interview, Kouchaki reveals that workers are 20-50 percent more likely to be dishonest in mid-to late-afternoon than in the morning and are less likely to exercise self-control after lunch. There is a “psychological depletion” of the resources needed for self-control as the day wears on resulting in poorer moral choices, she indicates. 

Ahh, now I get it! July is not about freedom from the daily grind! July is our month to re-build the mental resource muscles necessary to maintain self-control in order to stick to more moral behavior when the next season begins a month from now. Whew! 

Seems like a lot of responsibility is placed on the month of July if you ask me. Next October, when I am worn down by fatigue or discouraging events, will my self-control muscle exercises from July be enough to save me from the natural drift to unethical behavior? Probably not. July may be too far away to touch. 

Here are some suggestions from Kouchaki: Breaks from the routine of your day can serve the valuable purpose of restoring your depleted energy, positioning you to make better choices in the afternoon. She indicates that self-control is like a muscle – we need to restore its strength after use through an afternoon nap, rest, yoga, meditation, prayer, or an energy filled snack  (See my blog entry a few years ago on the need for Quadrant II time built into your day) all those things can help restore us back to more ethical behavior late in the day, week, month, or even  - the 2014-2015 season.  

Well, I am off to work out, and relax, so this blog entry must end. Gotta go get that ethical muscle exercised and renewed. August is just around the corner and my kids and colleagues are going to need me to be in shape! 


Monday, June 2, 2014

Graduation, Bridges and Bob Dylan!



A good friend and colleague sent me an email today with the subject line:  “MIA”.  Like many of my closer colleagues., she had not heard from me in a few weeks, and that did not seem normal. Although we are not from the texting/snapshot/twitter generation of instagram replies, we do manage to wade our way through these digital mediums. So, not responding in a few weeks seems like a life of time these days…

On this day, though, what I mostly am is inspired.

Inspired by the family in our lives and the way we are “crossing bridges” – some of our own choice and some not – this spring.  Our son crossed a bridge in his life four weeks ago – he left his life as a single man, and voluntarily crossed over the bridge to marriage.
Kind of like the game of “LIFE”.

He and his wonderful wife chose to walk over that bridge together, and both are forever changed. Their choice to cross the marriage bridge was on their own terms, but not all choices are that way.  

Last night our youngest daughter graduated from high school. It is a different sort of right of passage – a bridge that is as much about time as it is anything else. About being 18  years old. About being young and getting older. Without much choice, she sat at the graduation ceremony, in her robe, cap and tassel as this bridge in life roared up in front of her. She is crossing it, ready or not (so are we as her parents as our youngest child leaves us). High School is over. Her K-12 education is over. Her home life as she has known it, is over. The high school graduation bridge chose her last night. And there is no going back. No chance to be 6 years old and in 1st grade again. Time provides bridges that pull you forward.

Taking a look at the more than 445 graduates getting ready to cross the bridge, (Our daughter is right side, 1st row, 3rd from the end, (it's a where's Waldo test),
there are so many similarities with so many differences in each of the graduates. There is so much promise. So much hope. So much that is unknown. More opportunities for some than for others. So many more bridges that will be crossed.

And in between those bridges, the journey will be both glorious and painful, because it is a human journey. Choices they make will be both good and bad. And then another bridge will pop up and they will either choose it, or it will choose them. Job and career choices, post high school graduation choices, college choices, marriage partner choices, location and living choices, leaving home and going home choices. The bridges present themselves, and they decide "Do I cross or not" along the way of the journey.

Like most graduation ceremonies, the ”messages” that filled the air last night focused on “shape the world, don’t let it shape you”. There is a self-determined self-responsibility will in that message and that is good. Yet, I think the message should be “shape the world and let it shape you”. Understand how you both lead and serve in the greater community.  

And so the real choice for these graduates and for each of us, is about the journey between the bridges. How will you think of others and have them think of you? How will you treat others and have them treat you? I am pretty convinced these students will remember us not so much for what we did for them, they remember us for how we made them think and feel.  Actions are important; relationships even more so. They walk hand in hand or they don’t really walk the journey at all.

The life “bridge” moments we face are empty, if there is no joy, no youthful spirit along the journey. If somehow, as Bob Dylan reminded us, you don’t stay forever young. For the 18 year olds last night, can they find their inner 9- year old, that child that many of us as parents are clinging to as we also let go? For you and me, can we find the peace that comes with a youthful heart and spirit no matter what age and what bridge we need to cross next year? 

Click this link to listen to the song and watch as then 91- year old singer song writer Pete Seeger finds the joy in his journey, and his hope in the children of our future, singing Bob Dylan’s 1974 song Forever Young. The original song release coincides strangely enough with the end of my first year of teaching mathematics in a small rural Illinois town, many many bridges ago. 

This June, may we all have the courage to cross our bridges, and enjoy the journey, as in our hearts, we remain “Forever Young”!

 Dylan's original lyrics to the song


May god bless and keep you always
 May your wishes all come true
 May you always do for others 
And let others do for you
May you build a ladder to the stars 
And climb on every rung 
May you stay, forever young 
Forever Young. 
Forever Young
 May you stay forever young
May you grow up to be righteous
 May you grow up to be true
 May you always know the truth
 And see the lights surrounding you
May you always be courageous
 Stand upright and be strong
 And may you stay forever young
Forever young, forever young
 May you stay forever young
May your hands always be busy
 May your feet always be swift
 May you have a strong foundation 
When the winds of changes shift
May your heart always be joyful
 May your song always be sung
 And may you stay forever young
Forever young, forever young
 May you stay forever young



Wednesday, March 12, 2014

The Secret To Homework: It's Independent Practice!



I loved the article from CathyVatterott in Educational leadership this month! Just what we need to know: By using homework for practice in self-assessment and complex thinking skills, we can put students in charge of the learning process.

In my discipline – Mathematics - No more p. 238 5-57 the odds for assignments, no more 32 “drill and kill’ math worksheets, no more 90 minute homework assignments, no more going over homework the next day for 25 minutes of class, no more assigning homework at the last minute, no more students not knowing the answers and being able to check your work as you practice, no more homework filled with only lower level cognitive demand tasks! Homework will be worthy of our students’ best efforts? Right?


Not so fast.  

Is homework really an essential element to the process of student learning? The short answer is yes. But the best protocols to follow for homework are not quite as clear.

Mathematics homework is an area that often lacks clarity, purpose and certainty for your students, your parents, your schools’ intervention support personnel, and most importantly for you. Your team asks, “Why do we give students homework? What is the purpose of homework? Why won’t students do their homework? Why do we spend so much time going over homework in class? Why is homework assigned for a grade?” The very idea of homework, and what to do with it is often a conundrum for you, your team and for your students.

Here is what we do know: The assignment of homework can no longer be a superficial exercise for you or your team. My colleagues and I now think the “homework” you assign students, as well as the way you think about homework as an in-class activity is one of the most important team discussions you can have, for agreement, before the unit begins.

Research does indicate that homework can be helpful in improving student achievement if implemented correctly (Cooper, 2008).  Practice is important, but not without first developing student understanding in class.

Matt Larson, a national mathematics expert and lead author on our 2012 Common Core Mathematics in a PLC at Work series and our new 2014 handbook series on Beyond the Common Core in a PLC, suggests that student practice without understanding may be detrimental to students’ development of fluency, and in many cases avoiding this danger means that instruction should place greater emphasis on guided practice in class  – practice that is supported by monitoring and feedback – prior to independent practice outside of class
 
Research also supports the idea of spaced (sometimes called distributed or spiral) vs. massed homework practice during the unit of study (Hattie, 2012) as having a significant impact on student learning. That is, provide homework assignment (practice) tasks that are spaced throughout the unit, allowing your students to cycle back and perform distributed practice on prior learning standards, including those learned earlier in the unit, previous units, or possibly the previous grade level.

As each teacher on your team begins to honor teaching to the same set of essential learning standards and designing high quality common assessments for your grade level or course, then it is a natural outcome that the nature of independent practice for student learning outside of class (homework) would be designed from the same core set of problems for each student, no matter the assignment of teacher for the grade level or course.

Understanding the purpose of homework

This spring you can and should use the questions in the Collaborative Homework Assignment Protocol Discussion tool to help you and your team develops a better understanding of the purpose, the content and the expected protocols for the units’ homework assignments. Think of it as a sort of spring-cleaning of your current homework habits.

Collaborative Homework Assignment Protocol Discussion Tool

Directions: Work with your course level collaborative team to develop unit by-unit homework protocols for your course level.

Purpose of Homework:

1.     Why do we assign homework for the lessons of each unit? What is the fundamental purpose of homework?


Nature of Homework

2.     What is the proper number of practice problems (mathematical tasks) for daily homework assigned during the unit?



3.     What is the proper rigor (cognitive demand expectations) of the practice problems (mathematical tasks) for homework assigned during the unit?


4.     What is the proper distribution of practice problems or tasks for homework to ensure spaced practice for our students?



5.     How do our daily homework assignments align to the expectations of the essential learning standards for the unit? How do the students know this to be true?



6.     What steps shall we take to identify the homework (independent practice to be assigned and how will we communicate the assignments to students/parents/support staff?  How will we reach consensus on all unit homework assignments? How do we ensure coherence across the team to the student learning and practice expectations?


Use of Homework:

7.     How should we grade or score homework assignments during the unit? (What percent of a student’s total grade should be based on homework?)



8.     How will we “go over”, in class, the homework practice that is assigned to our students during the unit?

9. How will we communicate the Common Unit Homework Assignments to the students, parents and support staff, before the unit begins?




Mathematics homework should be a formative learning activity, i.e. an opportunity to obtain independent feedback and improve learning. Think: Primary purpose of mathematics homework is independent practice. More importantly, successful independent practice. That is, students must understand and use homework as an opportunity for formative assessment learning – while you are not in the room (Hattie, 2012).

Perhaps the homework paradigm shift for you and your colleagues is to stop calling it “homework”. Certainly “Independent Practice” can be done at the coffee shop, or after school in a classroom at school, or on the bus, or sitting in a hallway, or in the car on the way to practice or a game, or with friends at the library, or at the neighbors house. Independent practice does not have to be done at a specific location… it just has to be done.  

The work of your collaborative team is to decide, before the unit begins, what and how much homework to provide for additional student independent practice. Your team must decide how you will communicate the homework assignments to students and parents. And your team must decide the role homework plays as part of your classroom protocols.

Using effective homework protocols


1. Homework purpose: The primary purpose of homework is to allow the student the opportunity for independent practice on essential learning standards mastered in class. Homework can also provide a chance for the student to practice mathematical tasks that relate to previous learning standards or tasks that reflect prerequisites learning standards for the next unit.

2. Homework length of time: How much time should daily homework take students to complete? How many problems should it entail? Homework should not be lengthy (Cooper, 2008) so care should be given in what is assigned. Take into account the cognitive demand level of the tasks or problems assigned. Think no more than 25-30 minutes K-5 and 35-45 minutes grades 6-12 of student time outside of class each day.

3. Homework problem set/task selection: Homework that provides review of previous work and helps to prepare for work to come has been linked to improved student achievement as well (Cooper, 2008). Make sure that all tasks/problems assigned are necessary as part of independent practice, ensure there is spaced practice and not massed practice, and make sure that the tasks assigned for homework actually align to the essential learning standards of the unit.

4. Providing Homework answers:  When Students are provided answers to the homework problems they can check their solutions against the answers, and if their end result does not match the provided answer, they to rework the problem to find their error. In other words, students receive immediate and formative self-assessed feedback of their work (similar to what happens when playing an electronic game). Moreover, a compelling reason to provide students the answers to the homework in advance of the assignment is the time saved not giving out answers during the class period.

5. The role of homework in class: Once the homework to be assigned is determined (before the unit begins), your collaborative team’s discussion should focus on how the homework will be addressed in class, the type of feedback that will be given to students, and what will occur if students do not complete the homework. If most of the class time the next day is spent going over the homework then you lose the impact of successful independent practice on student learning. Your students may be choosing to wait to do homework problems, precisely because they know you will go over the problems the next day. Since the purpose of homework is independent practice, limit the amount of time given in class to grade, score, or go over the practice problems. These daily and unit processes and procedures should be consistent from teacher to teacher within your collaborative team.

Final Thoughts: Why are students expected to do homework? Not because they will receive a grade, not because they hope you will “go over” the problems in class the next day (which makes homework no longer an independent practice exercise), not because they are being punished. 

Only because your students understand the importance of “formative assessment” and successful practice as a critical aspect of their long term memory learning process.


In class students do need your teacher modeling and lots of peer-to-peer guided practice, then out of class, and in a timely fashion, they need to do accurate independent practice with feedback (self-feedback and action or with peers) – well before they are back in your class the next day.

I wish you the best in your homework, oops, independent practice, journey. I hope these protocols and guidelines help as you think through this often-difficult aspect of your teaching and leading students!