Achievement Level Descriptors (& what your actions tell students)

I am currently the President of the Minnesota Council of Teachers of Mathematics (MCTM).  As part of this role I write a monthly article for our organizations online mathematics magazine, MathBits.  Last year I wrote an article about my FAVORITE math task and the magical sweet spot in teaching.  It’s a great article – you should read it – you can find it HERE.  My goal in writing this was to encourage MN math teachers to select tasks that are mathematically rich and result in student discourse and engagement.

In this post I want to revisit the task I mentioned in the article above to make a different point.  I am going to warn you.  I am going to get super preachy in a couple of paragraphs from now.  For those of you that know me – imagine me standing up waving my arms – pointing – and over and over again telling you what to do.  I am so passionate about this topic.  I can not stay silent any longer.   Our actions as educators speak more loudly to our students than the words we say and I want to call out and encourage all of us to look at one action we may be engaging in that is saying something to our students that is pretty heartbreaking.

For 5 years I worked at the district office of a large urban district.  During my time working downtown I observed hundreds of classrooms and looked at the testing data of hundreds of teachers.  I was fortunate to  observe amazing teachers doing amazing things with students day in and day out.  But I also saw one common trend in my district that still exists today and discourages me like no other thing I see.  I have seen this happen in ‘out of control classrooms’ and in classrooms of teachers who were amazing managers of students, creative, funny, & engaging.  I’ve seen this happen in my own classroom. One thing I know for sure, this is not just a MN problem, this is an everywhere problem.

In too many classrooms I walk into the mathematics being taught is well below grade level.  In many classrooms 25%-75% of the year’s material is at least one grade level below where it should be.  Things that were taught and tested in Middle School are retaught and tested in High School.  This comes at the cost of teaching grade level material.  Many teachers are weeks, months behind pacing schedules (to make ourselves feel better we call them racing schedules).  Sometimes teachers end the year only having taught 1/3 or 1/2 of what they should have.  We end up teaching only skills (’cause their faster and easier) at the expense of students mastering concepts.   We make excuses for this and yes I totally get why we do this.  Many students enter our classrooms unprepared for the math they will see.  This post is not about all those reasons – this post is what our actions are saying to students.

soapboxYou’ve been warned. Here is where I get on my soapbox.  I can not say this loudly enough.  Please hear me.  When we as teachers do not teach all grade level standards to our students…. when we as teachers do not figure out ways to assure all students have an access points to the tasks we select so they can make growth on grade level standards….What our actions are saying to students is “You don’t get to go to college and be successful because I the adult decided to not teach you grade level standards.  I have put you in a position where you will continually be behind.  You may get into a college but more than likely you will fail the math test they give you upon entering and have to take a course in which you pay for (or use up scholarship money on) and get no credit for.  You don’t get to be successful in college and my actions made that decision for you”. I know this is so blunt.  So so blunt.  But I am too old to wait for us to talk about the elephant in the room.  I want to shake us out of our well meaning desire to support struggling in ways that feel good in the moment but do not result in success years later.  There are things we as math teachers can do to assure more of our students are successful.  It is hard.  It can feel impossible, but it is possible.

Think about what the students in the courses we teach look like that are receiving below grade level instruction in their core math class.  If your district is like mine, this alone speaks to many of the gaps that exist in our systems.  Our compassionate sides are thinking we are helping students by giving them instruction ‘at their level’, but we are setting them up for future failure.  (Before you start – yep I know I am over simplifying this to make it work in a post and yep I know there are examples of where this is not true and…and..and… – please though stop and just ponder if what I am saying might be true for even 1 or 2 students at your site.  If it is, please consider what you might do differently).

3 years ago when I returned to the classroom I committed (and got my teaching peers around me to commit to) making sure every student at my school received grade level instruction on core material.  This was our goal and focus throughout our year during team meetings.  Last year one of my peers said to me at the end of the year (after looking at her data) “Sara, I did not think it would work to teach all students grade level material, but look at my data – the largest growth was with my lowest level students. Why isn’t every teacher doing this.”.  I am not going to lie to you, it is not easy – but there are simple things we can do.  Let me tell you one story to paint a picture for you.

My favorite 7th grade task was the first one I used in our statistics unit.  I assigned this task to the class on day one and got them to work.


As soon as I assigned the task many hands went up.  Students asked me how to find ‘mean’, ‘median’ and ‘range’.  I simply shrugged and told them to look it up.  My student had iPads – but if they did not I would tell them to get out their phones.  Within minutes all partner groups had retaught themselves these skills.  I did not have to reteach them how to do this, they looked it up and taught themselves.  My students did have access on my schools website a 50 page 7th grade resource book of vocabulary and more – but some used their friend ‘google’.  25 minutes later all students presented solutions to this task.  This was day one of the unit.

Many 7th grade (and let’s be honest HS) classroostandardsms reteach students how to calculate mean and median.  Teachers provide countless worksheets where students happily repeat learning this skill.  This takes days and sometimes weeks to reteach. Too often we assume we will have to review old skills without even checking if this is true.  Worse, sometimes we read standards and assume that it is grade level to teach calculating the mean at 7th grade.  Let’s look at the MN 7th grade standards.  Notice that it is a MN 5th grade standard to calculate the mean.  In 7th grade students will be assessed on their ability to describe the impact of inserting or deleting a point had on the mean.  Think about the tasks you are using with students.  Are they grade level?

As a math leader in MN I have encouraged teachers to read the grade level standards they teach at least 4 times a year.  Often we do not teach what we should simply because we are unaware.  I encourage teachers to print out the standards and hang them next to their desk.  I encourage teachers to keep an extra copy at their home.  Happily for me, I see teachers doing this all the time.

What I have come to realize though is that teachers don’t know that the State of MN also has something called ‘Achievement Level Descriptors‘ (ALD’s) that describe the types of questions students have mastered as represented by their scores on our state assessments.  Let’s look at the Data Analysis and Probability ALD’s for 7th grade.ald highlighted

Notice the difference between what I’ve highlighted in yellow and green.  Too many of us 7th grade teachers are only providing instruction at the ‘yellow’ level (and maybe an question or two at the ‘green’ level) and we wonder why our students continue to do so poorly.   How can students improve if the amount of time we spend on the ‘yellow’ parts far outweighs the amount of time spent on the ‘green’ parts above.

I get asked by principals all the time what their school can do to improve their sites testing data.  I give a common message each time.  Look at the level of math being taught to your lowest level students.  In most schools I’ve been called into, their 7th grade students are only being taught how to calculate the mean (over and over again).  They get lots of practice at it.  They think they are teaching grade level standards but they are teaching them at a level that assures all students will continue to ‘not meet standards’.  Schools scratch their heads wondering what they are dong wrong and it is pretty simple – they are not teaching ALL students  ALL grade level standards at a level they can be proficient at.  How can we expect students to be proficient and grow if we the adults have decided for students that they will not even get exposure to grade level material?

If I could encourage all teachers to do one thing, it would be to commit to making sure all students have access to rich mathematical instruction at their grade level.  Believe it is possible and act as it is.  Change the focus of you professional learning communities to creating tasks that have multiple entry points so all students can grow at (or beyond) grade level.  Work to create supports for students who are not at grade level.  Make sure though that these supports do not include removing them from core grade level instruction.

The teachers making the most growth with all students in Minnesota are doing this.  It is possible.  An easy way to start is to read the MN Achievement Level Descriptors and Standards.  I have provided them for you below.  I encourage you to make sure your actions with students match what we are all saying to our students: ‘I believe everyone of you can learn mathematics’.

OK, I will get off my soapbox for now.  Thank you for indulging me if you have read this far.

Resources for MN Teachers (for you CCSS states, I am sure you all have similar things to guide you – look for them and use them).

ACHIEVEMENT LEVEL DESCRIPTORS (MINNESOTA)  Ask yourself “Am I teaching at a level so that ALL students had a chance to become proficient on grade level standards”.

STANDARDS (MINNESOTA) – You must read these at least 4 times a year.  Print them out and read them. Make a plan so that ALL students will have exposure to ALL grade level standards.  ALL of them.  The K-High School standards are located (scroll to the bottom) of another post located HERE.  Download, print and read.  It only takes 15 minutes to read one grade level standards.

Sara VanDerWerf

I am Sara Van Der Werf, a 24-year mathematics teacher in Minneapolis Public Schools. I have taught math in grades 7-12 as well as spent several years leading mathematics at the district office. I currently teach Advanced Algebra at South High School and I'm also the current President of the Minnesota Council of Teachers of Mathematics (MCTM). I am passionate about encouraging and connecting with mathematics teachers. I'd love to connect via twitter.  Join the community.  Tweet me @saravdwerf.

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