Category Archives: High School Math

Formative Assessment -> Follow-up Action

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During a conversation with @druinok this past weekend – about an upcoming PD session she is co-leading, I was reminded of this post…

Using In-Class Formative Assessment Effectively

After re-reading it a couple of times, I almost think I should set a reminder to revisit is every few weeks.  All the things I thought I knew about Formative Assessment in the past years, I am finally having a break-through of understanding what its really all about.

Don’t get me wrong – I’ve had the knowledge and said I agreed.  I know it benefits learning when used to inform instruction.  I’m just not sure all of my actions have been supported by a true, internal understanding.  The how-to’s, why’s and other questions I’ve muddled through in recent years are finally sinking in.

As I mentioned in the linked post, for years I’ve searched for FA strategies – but the session with Dr. Kanold last summer helped me realize all I found were the tools I would use to gather the evidence from students.  The Formative Assessment is none of those things – the FA is the planned Follow-up Action.

The follow up action is something I’ve been aware of for years… look at this “old” unit organizer… the peacock blue highlight on the right side.  self-assessment

What I have internalized about the Follow-up Action is that students in 9th grade may have not developed an internal self-check, as the teacher, it is my responsibility to help them develop this habit.

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The couple of months, I have been re-reading Embedding Formative Assessment with @druinok and some big a-ha’s for me.  She has a great post to sum up when I’ve realized with feedback here.

The only thing that matters with feedback is the reaction of the recipient.  No matter how well designed, if the student doesn’t act on it, then the feedback was a waste of time.  And..

Don’t give feedback unless you allocate class time for students to respond.  If it’s worth your time to generate the feedback, it’s worth taking instruction time to ensure students respond.

If I give them feedback, and I want them to act on it, then I must provide them with time / structure to do so.  Is the feedback given in such a way, they can respond to it?  This semester, I have been very intentional with this.  It may seem like a generic structure, but it has given us a starting spot…

  • A couple of silent minutes to read / process the written feedback.
  • A couple of minutes to respond / redo / revisit the learning task / assessment question in writing.
  • A couple of minutes to discuss with their shoulder partners.
  • Then ask questions of me.

The Follow-up Action is the essence of Formative Assessment.  I am guilty in the past of doing formative assessment, but never using it to inform my instruction.  Yep, check that off the list, formative assessment complete.  Yikes.  I don’t think I am the only one.  We feel chained to the pacing guides, like we must keep moving.  That is the failure of education.  We have let this steal our students’ opportunities to learn.  I must keep reminding myself often –

Less can be more if I do Less better.

If I am serious about student learning.  If I walk my talk.  I am no longer doing for the sake of doing.  I am no longer adding a task to my lesson plan to check off the box for admin to see.  I am choosing intentionally.  I will plan those Formative Assessments, and truly use the information they have gathered.  I will allow myself the room / time to go off the lesson plan and pacing guide and do what’s best for my kids.

In doing this, I believe it takes away some of the anxiety students experience.  I believe it opens the classroom to becoming a safe environment for making mistakes and learning.  In the past I’ve claimed to celebrate mistakes as learning experiences, but I am not sure that message has transcended to my learners.

I will plan a purposeful, intentional follow-up action, then allow my students time to react/respond to it…  I am giving them time to process, make sense of and iron out those misconceptions, redo their mistakes, making note of them – allowing them to see, observe quality student work and examples – providing them with models to help build better understanding.

 

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How I Quit “Wanting to Do It All” #MTBoSBlog18 February

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Earlier in the year, a colleague and I created a shared a folder on drive to collect our resources for Algebra I.  The really was not new – we’ve had dropboxes, shared folders in outlook, etc. before.  The shared folder had sub folders for each unit of study.  The problem was, when we started dumping files in – well, I knew which ones were mine and what they were for – but I had no clue what the shared files were all about.  And the same on my colleague’s end as well.

After meeting, we agreed to creating sub folders in each unit:  Lesson Notes / INBs – foldables;  Practice tasks/ Skills development;  Formative Assessments; Summative Assessments / Projects.  We devised a file naming system – targeted the Unit Name, Lesson / concept title, what the task was specficially.  Though it has helped, it has really brought to light something I struggled with years ago.

I began feeling overwhelmed – sometime during the peak of Pinterest – Oh that’s so cool, I’ve got to do that!  I love that idea – yep, gotta add that to the unit.  Yes!  Another game or sorting task – add it too!  Add them all!  And that is when I began falling.  I had become a hoarder teacher – what?  Yep, I wanted to collect AND use ALL of the activities.  And at some point, I believe I really tried to do just that.  Noone questioned me.  Noone asked the tough questions – of why / purpose of the task.  I just did everything that looked fun.

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Somewhere along the way, looking down at a never-ending list of activities on our unit organizer one day, I asked myself – what has happened? How do I eliminate from the list?  All I wanted was to engage learners.  But were they really learning what I had intended to teach?  I over planned – too much stuff.  But I loved it all.  So much of it was truly effective – or so I thought – but there simply was not enough time to do.it.all.  Something had to change.  It was me.

I began asking myself several questions as I scrolled through the lists –

  1.  Does this really teach/help students learn a target?  Or it is just something I love doing, its fun, but does it really focus on a given standard for my course?
  2. How can I reorganize the task – in a way that allows it to efficiently help students work toward our given goal?
  3. Do I have real evidence that this task is truly impacting student learning in a positive way?
  4. What exactly will students know and be able to do / better understand after completing this task?
  5. Does this task have a good reflection built in?  Do I need to create one?  How can we revisit the big ideas of the task and make connections both mathematically, between student ideas and even to contexts outside of math class?
  6. When I have two equally good tasks – how do I choose between them?  The answer is simply – look to my students.  Chances are I have used the tasks in the past – I know which type of learner a task is best suited for.   Heck, I may use one of them during 2nd block and the other one during 4th.  It really is whatever is best for students.

Though it has been difficult to let go, I have slowly begun to choose more purposeful tasks when planning the unit.  But I’ve placed the “old” tasks in a digital folder within the unit – which will give me another resource, should my choices not benefit a particular group of students.

A true backwards planning has helped me follow-through.  My colleague and I have a list of targets – we tweak and update versions of assessments – to ensure we have the end in mind.  Every question falls under a section titled with the intended learning targets.  We discuss the purpose of every question and what we are wanting to see about student learning – is it assessing what we think/thought it was?

It is from here, I can begin analyzing a task, before I add it to our unit schedule.  And I start with this question –

What is the purpose of the activity? 

 Is it for learning?

    • A foldable for summarizing notes / big ideas?
    • A foldable / other INB insert to organize some examples of situations / problems to solve?
    • A vocabulary – activity?
    • An investigation?
    • Scaffolded discovery activity?
    • Problem solving task for small groups?

Is it for assessment?

    • A check for understanding that leads to formative assessment?
    • If so, how will I know that they know if I choose to use this task?
    • What is/will be the follow up action if they don’t know?

Is it for practice? 

    • Skills development?
    • Applying vocabulary?
    • Transferring ideas to other contexts / learning?

When I decide the purpose of the activity, I am more able to know where it should be placed in the sequence of learning.  It is true, many of these tasks have multi-fold purposes – now I specifically note what I will use it for and how it will inform my instruction, what actions should follow in certain situations.

In doing this, I have had to let go of some of my favorite tasks from years past because they were not doing what I needed them to do.  I did not dispose of them completely – because with work, I believe some will be worthy and more purposed for using again.

The other tough thing is – when I do run across an amazing idea – I have to let something else go.  Will this new task be better than the old one?  How will it get across the big ideas?  How will I know students have learned?  But the reality is, I cannot do it all.

Now, when I look at an activity and run through these questions – I try to figure out why I used it to begin with and is it able to move students in the right direction.  Now I am becoming more aware of the the differences in activities and their purposes.  I can be more confident in the usefulness of what I am choosing and have greater impact on student learning.

What challenges have you run into when planning your lessons and units?  How do you determine the better learning task?  What suggestions would you make to someone who is trying to “use it all”?

Something Old, Something New…

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I used to keep a large poster up for our INBs table of contents.  For whatever reason, I got away from that last year and did not even do it last fall with those classes.  However, the poor attendance, numerous snow days have demanded I do it again…  to help students get / stay organized / catch up and for my own sanity!  When they ask…I can point to the poster…

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Something new…  I am a believer in literacy strategies.  Students often are not taught how to take notes from what they read.  Most of us vomited highlighter all over our textbooks…  without discerning the needed, important information, we would just learn ALL of it.

So, here is what I did…  Students are 4 to a table, so I cut the review / summary notes into 4 sections.  I asked students to divide their pages into 4 sections with labels.

Each person at the table gets a different section of summary notes / examples.

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This was over domain and range of continuous graphs.  With a snow day making a long weekend, I thought it was a great way to review.

1 minute to read.  1 minute to jot down important BIG ideas.

Rotate summary notes.

Repeat.

Some may think 1 minute was not enough time – but since this was a review of last week’s work, I felt it was fine.  If introducing new material, I may feel differently.

After the first round, I observed students writing during the reading time.  I shared my reasoning – the first time was to read – no worries about grabbing information to remember.  The second time was to skim / write big ideas… that way they were accessing the information at least twice.

After every student has read / written for all 4 sections.  They share out 1 BIG idea they wrote down with their table.

I asked for questions, but none.  So, I think next time I will have a post-it available to reflect…  something I learned, realized, was reminded of OR still have a question about…  they tend to ask when its written and anonymous.  I get that.

What summary, literacy, reading strategies do you use in math class?

 

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Accountability – Reflection on My 2018 Spring Goals

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A full week of school – the first weeks, though one was fairly productively – in and out with snow days, well – no consistency.  We were out the entire week last week – with MLKjr Day and the snow / cold temps.  So this week meant collecting and giving feedback on NTI day assignments.  Not my favorite task at all.  One class was fine- I had about 4 students having to redo assignments because they were not proficient.  The other class, I had about 4 students needing to redo, and 9! Students who did not even do the first assignment.  Phone calls and emails home…  ugh.

With all of that – we sort of got back into a routine.  So I felt it was time to reflect on my semester goals.  This post describes my goals as a result of a conversation with @misscalcul8.  Here’s the jist:

For the Spring 2018 Semester, in my 4th block Algebra I class, I will increase (currently, I do not link them in my plans) my planning of formative assessments for each learning target listed / linked in my unit lesson plans.  Twice per week, I will take time to formally reflect (written) the student work and devise a plan for next steps.   Currently, I only informally reflect / plan next steps, without formal documentation in my plans.  I hope this work will lead to better quality formative assessments that are truly at the level and integrity of the standards.

Over the course of the Spring 2018 Semester, I will develop a list of common Latin / Greek roots as related to our content in Algebra I.  Through the collaboration of my colleague, I will develop and implement a weekly system to help students learn and make connections within the content to the roots, etc.   The list, weekly quiz results and study tools will be documented in lesson plans.  At the end of each month (January – April), I will reflect on our progress, analyze the impact on student learning and adjust, continue.  This list should grow throughout the semester.  List to students, implement study tool, report student progress.

I will revisit Small & Lin’s book More Good Questions for ideas on creating Open Questions.  As part of the formative assessment tools, I will begin to include these on a weekly basis in our lessons – for feedback only and incorporate on every unit assessment (after discussing with my content team teacher).

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Where Am I?

As part of our NTI PLC time, we spent time building a document to list each of our learning targets, CCSS for searching resources and link FAs documents / describe the task for each.  This was not necessarily “IN” my weekly lesson plans, but it is a living document that can easily be linked to.  I can quickly copy/paste the linking information into my lesson plans.

As part of this task – my colleague and I met, devising a system for naming our resource files as we upload them to a shared folder.  We agreed on 3 letter abbreviation for BIG idea of the unit, then use 2 digits for the learning targets.  For example, FUN 01 means intro to functions, learning target 1.  This way we can record in the IC which target that “grade” is addressing for parent and student communication.  Students receive a unit organizer at the beginning of the unit with ALL of the assessment targets listed.

Inside each folder, she suggested having sub-folders:  one for lessons, INB foldables, example for notes, practice tasks like matching or sorting;  one for FA tasks;  Summative and projects folder which will also include a unit pre-assessment and multiple versions of the unit assessment.

We have just a few more things to have everything addressed in our current unit.  We think this document can easily be added to and edited as we go through the units – adding new things, etc.  Targets highlighted in red if we need to create a better target quiz, we can quickly scan to see where we are and what we need to do.  We have a lesson plan outlined for the operations with functions target, but need to create a TQ.

Since starting our document, we have found an example from the Springboard resources that can serve as a skeleton for identifying and relating key features to the context.

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From Springboard, Algebra I

 

I have done nothing with the Roots list in vocabulary.  Every unit organizer has listed vocabulary – so I am hoping to use these as I begin to develop this list.

I used one open question for a TQ this week and gave immediate verbal feedback to students with high give/thumbs up or questions/coaching.

What can I celebrate?

Getting on the same page with my colleague.  We have a plan in place.  We’ve started organizing our current resources and agree as we continue in the semester, we can easily add and adjust.  I like our system for highlighting places that need work and the ability to share found resources as we use them.

I was very purposeful in the FA used in class this week.  Even with the deltamath and desmos tasks in the lab on Friday have given me some conversation and lesson material as we move on this week.

What can I improve?

Ensuring that I have time built in for students to act on the written feedback.

Getting started with those root word lists.

Purposeful planning with the open questions – allow students to become comfortable with this style of questioning – you can tell its unfamiliar for some of them – but using strategies like “3 things” notice/wonder will help them build confidence in sharing their thinking.  I am already seeing more details in what they are writing and sharing.  I know this sounds silly, but I have noticed eyebrows raising as I put the task out there – almost as if they welcome the opportunity to think and share their thinking.

So where are you in your goals for this school year?  What are your goals?  What are you doing to be accountable to them?  Where are you?  What can you celebrate?  What can you improve?

Reflecting on Formative Assessments

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Every Story has a Graph / Target Quiz

Earlier this week, I gave a short Target Quiz – just one big idea.Students were given three scenarios and asked to create a graph to model the situation.  Out of the class, there were 4 students I felt I needed to pull over to the side for some one on one time.  I found they were often drawing the “shape” of what was happening rather than comparing the distance from home to time.

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The one most missed had Tom walking up a hill, quickly across the top, then ran down the other side.  Yes, most kids draw the shape of the hill.  As opposed to the distance continuing to increase as he ran down the other side.

Whiteboarding Examples / Non-examples

The second Target Quiz was on whiteboards – students had to create an example of a graph, set of ordered pairs and a table of values with a function and not a function in each example.

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I laughed as one table was begging me to give “real quiz” and take a grade because they knew that they knew!!  As I walked around the room, observing, asking questions – there were 3 students with some minor mistakes and 3 who were really struggling.  Upon questioning, they were able to identify when the example was given, but unable to create examples on their own.  With some “funneling”  – they were able to get examples of each, but I have them * to keep an eye on and requiz next week.

Deltamath Practice – immediate feedback from tech;

Teacher observation & questioning

We had a very brief introduction to writing domain and range of graphs in interval notation.  We spent some time in the computer lab today practicing this on deltamath.com.   I appreciate the immediate feedback they are able to see if they miss the question.  Also, how he has programmed the many different options for defining domain and range.

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Many misconceptions were cleared as we learned whether to use the endpoints or extreme values (if they were not the same).  There was discussion about the open circles and closed circles and which inequality symbols were correct to use and when.  And yes, a few realized they were mixing up the x and y for domain or range.  I look forward to practicing this skill Monday after their experiences today.

Desmos Activity – Inequalities on a Number Line – Matching Tasks

For my other class, we will be solving and graphing inequalities next week.  So while in the lab today, we worked on Desmos – Inequalities on a Number Line and Compound Inequalities.  The first task was a good review and learning opportunity for the direction of the symbols.  I still had some students exchanging those up.  Most were correct in open versus closed circles and what that meant in symbol terms.  Though I did not make it to all of the students in the second task – I was trying to catch students on the two sorting pages of the first activity as they were going through.  For some it was as simple as a brief discussion about why one was the correct choice and comparing it to their wrong match.  There are about 4 students still having troubles on the first task.  And several have not completed the last task.

I feel like looking at their responses, I can use their examples as discussion pieces while we are looking at our notes next week.

I almost feel like there were not as many issues in the second task.  However, I still have several that have not completed them yet.  But I feel like using live examples from their work and discussing maybe two stars and a wish they would have for each student – may help them steer away from making their own mistakes.

I love the real time feedback I get as a teacher and how I am able to grab kids before they move on too far and help erase some of their thinking and replaced it with correct ideas immediately.

Someday – I’ll get to have a classroom lab… I hope.  Until then, we will keep on doing what we can.

 

Heartbroken.

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Heartbroken. Angry. Apalled when I see those on social media making these tragedies about something other than they are. Heartbroken. I’ve cried – as a mom. I’ve cried – as a teacher. I’ve cried – as a friend of first responders and medical caregivers. This post by a middle school Social Studies teacher touched what […]