Target Based Grading v1.0: 2019-2020

In this blog post, I will detail why and how I implemented a target based grading system in geometry this past year.  I will share my thoughts and reflections about what went well, what didn't, and what changes I'm contemplating for next year.

I've been meaning to write this blog post for many months.  I gave a presentation at the SD STEM ED conference in February about this topic, and there was a high level of interest about it.  Thanks to being stuck at home for the past seven weeks, I've found a bit of time to write this post.

I typically blog as a vehicle for self reflection.  When I have a lot going on in my brain, I find the process of writing something semi-coherent helps me organize my thoughts and think more deeply about things.

That said, I am very interested in hearing feedback about my target-based grading system as I begin to prepare for next year and target based grading v2.0.  Please do not hesitate to comment, question, or push back on this post.  I welcome the discussion around the topic of grading.

(Note: S/O to my colleague Jarrod for joining me on this journey.  We continue to work in tandem and mirror each other day by day and are both better for it.  A majority of this process was "we" instead of "I".)


Part I.  WHY

My decision to implement a target based grading system was influenced by a number of factors.

• I've always been intrigued by standards based grading, dating back to somewhere around 2014.  I implemented a standards based grading system as part of my Master's action research during the 2014-15 school year.  I didn't love the grading system I used for the action research, so I stopped using it after one year.  But I was still intrigued by standards based grading.
• In my school district, the K-3 elementary buildings began using standards based report cards in about 2016-17.  I enjoyed seeing my children's standards based report cards compared to a traditional report card and continued to be intrigued.
• In 2017-18, my district began to implement what we are calling "mass customized learning (MCL)" in the K-3 buildings.  In 2018-19, MCL began in the Intermediate (4-5) building.  In 2019-20, MCL began in the Middle School (6th grade class).  It is scheduled to arrive at my high school in 2022-23.  MCL is centered on students demonstrating mastery of learning targets, which are written in student-friendly "I can..." statements.  One of the components of MCL is assessing (and reporting) student growth on the learning targets.  In other words, MCL and target based grading go hand in hand.
• I read Jo Boaler's Mathematical Mindsets and was convinced that traditional grading and assessing has some negative consequences.  Boaler talks about assessment for learning and gives some advice on grading.  The target based grading system that I hoped to implement followed many of Boaler's guidelines.
• One recommendation that Boaler makes is to not include homework as part of a student's grade.  She makes a convincing argument that grading homework is an inequitable practice.
• In past years, I have graded homework a number of different ways.  Some years, I would have students do a self-check and report their score.  Other years, I would collect and grade the homework on completion and/or accuracy.  Either way, homework has been graded and counted between 15-25% of the student's grade.  Recently, I grew tired of students copying answers or being dishonest when they self-graded.  It wasn't all students each year, but a growing percentage of students.  I was ready to completely remove the homework component from a student's grade.
• In 2018-19, I participated in a leadership cohort (called SDMath/Sci) through the South Dakota DOE.  It was some of the best professional development I have ever been a part of.  We learned about a leadership theory by Simon Sinek centered on "Finding Your WHY".  Equity was a major component of the training.  Echoing Boaler's claims about equity, the cohort opened my eyes to some of the systemic structures that are a part of our educational system.  Traditional grading practices were something we discussed.  I had found my WHY: a target based system would create a more equitable way of assessing the students in my classroom. 

Part II.  Setup

Target Based Grading vs. Standards Based Grading
I mentioned earlier that I didn't love the standards based grading system that I had implemented for my action research.  At the time, South Dakota had adopted the Common Core State Standards.  I felt that certain standards were too broad to accurately assess student understanding.

Take Standard F.IF.C.7.B for instance:

Graphing square roots functions, cube root functions, and piece-wise defined functions (including absolute value functions) were all topics I covered in Algebra 2.  I claim that there are potentially students who have full understanding of graphing square root and cube root functions, but who struggle to graph piecewise functions.  And vice-versa.  In a standards based grading system, what sort of grade should those students get?  If I'm using a 4.0 scale, would that student earn a 2.0?  A 2.5?  Would those scores truly reflect what the student understands?

That ambiguity helped me decide that I wanted a target based grading system, where I assess students on each learning target.  So last summer I created the complete list of learning targets that I wanted to assess for geometry.  [Geometry Learning Targets]
Note: I am already in the process of tweaking this list for next year.  I realized that I needed to combine some targets together, especially in the surface area / volume unit.  I also plan to re-sequence a few of the targets.


Learning Target Quizzes
Each learning target was assessed on an in-class QUIZ.  Each quiz had between two and five learning targets on it.  The quizzes were designed to be completed within one 50-minute class period.

Example: This is Quiz #5, which assess learning targets 16-19.

A couple of things are worth noting as you glance through the quiz.

• Students are scored on a 0.0 to 3.0 scale.  A score of 0.0 is given if a student does not complete the questions for that target or demonstrates absolutely no understanding of the target.
• Students cannot earn a score of 0.5.  I don't have any good reason why that score wasn't allowed other than I felt that if a student gave full effort and demonstrated some level of understanding, a minimum score of 1.0 was valid.
• The difference between scores of 1.5 vs. 2.0 vs. 2.5 varied by learning target.  Some learning targets had only one question to answer (see target 19 above), while others had up to five questions to answer.  
• A score of 3.0 demonstrated quiz mastery.

Retake Policy & Process

If a student earned less than a 3.0 on any target target, they were expected to retake the part of the quiz aligned to the target.  

There was the process to completing a quiz retake.

1. Error analysis & reflection: For each target needing re-assessing, students completed a Quiz Correction Form (see below).
2. Practice & study: Students were encouraged to review the practice problems and previous quiz before retaking.
3. Retake: Students could come into my classroom any time throughout the day to retake, even if I had other class in session.

Students stapled their quiz to the quiz correction form(s) and turned them into me.  I would check to make sure students had correctly completed the problems on the quiz correction form.  If they did so, I would use a rubber stamp to "stamp" their correction form, indicating that they had earned the opportunity to retake that learning target assessment.  "Stamped" forms were returned to students to be able to review and study from.  If there were errors made on the quiz correction form, I would return the form back to the student for revision.

When a student completed a retake of any learning target, the new score replaced the old score.  It rarely happened, but students could earn a lower score on their retake.

If a student did not yet earn a score of 3.0 after retaking the assessment once, then a second retake was available.  Before the second retake, I would have a one-on-one help session with the student instead of repeating the quiz correction form process.  The help sessions were typically fairly brief (between 3-10 minutes) and took place whenever there was enough free time to have one (before or after school, during my planning periods, or even between class periods).  

Quizzes were graded and returned to students the next day.  Students then typically had 10 calendar days to complete the quiz retake process.  I know that some standard-based grading systems call for students to be able to retake / improve their scores for as long as needed (or at least until the end of the semester or grading period).  I struggle to see the benefit of that theory for mathematics classes.  So much of mathematics builds on prior knowledge in a logical & sequential manner.  I need my students to gain understanding of the learning targets in a timely manner so that they will possess the prior knowledge needed for the next set of learning targets.  Therefore, I set a retake deadline for each set of learning targets.


Enrichment Tasks
After a student earned a 3.0 to demonstrate quiz mastery, they had an opportunity to earn a 4.0 and enrich their understanding.  For each learning target, I created an enrichment task.  Enrichment tasks were intended to deepen understanding and extend thinking.  Enrichment tasks were released (via Google Classroom) to all students on the day of the quiz.  Students could work on the enrichment tasks individually or with partners / in small groups; each student had to turn in their own copy of the task for credit.  Enrichment tasks followed the same deadline as the quiz retake.

Examples of the enrichment tasks for learning targets 16-19:

More things worth noting about the enrichment tasks:

• Students could earn scores of "Not Yet", 3.5, and 4.0.  (Recall: in order to submit an enrichment task, students must have first earned a 3.0 on the quiz.)
• Enrichment tasks were not a one-and-done deal.  If a student submitted work that wasn't correct, I would give feedback and allow students to fix their mistakes.  There were many occasions where a student earned a score of "Not Yet" or 3.5, I gave feedback, and they made revisions and ultimately earned a 4.0.
• The content on the tasks varied in nature, depending on the learning target.  Sometimes the enrichment task would include a problem or two that involved a little tougher algebra (see learning target 16 - solving a quadratic equation and considering extraneous solutions).  Other times the task might be to research some deeper idea that we simply don't cover in our regular instruction (see learning target 17 - considering spherical geometry).  

Grade Conversion:
In an ideal target based grading system, I wouldn't have to report traditional A-B-C-D-F grades.  Unfortunately, my district requires me to because we need to report things like GPA and class rank.  Boooooo!

I needed to create a way to convert the target based scores into traditional grades.

Before I forget, here is the grading scale for my school.

As you can see, semester grades were calculated by a weighted average of the quarter grades (40% each) and the semester final tasks (20%).

Quarter grades were calculated by a weighted average of the learning target assessments (80%) and miscellaneous tasks (20%).

Learning Target Assessments (80% of quarter grade):
Each quarter, all of the learning target scores were averaged to create an "Average Target Score".  The Average Target Score was then converted using this conversion chart.

Notice:

• Students needed an average score of 2.0 or higher to earn a passing grade in the "Learning Target Assessments" category.
• An average score of 3.0 earned a student a B+ in the "Learning Target Assessments" category.  In order to earn an A in the category, some enrichment tasks needed to be completed.

I used a Google Sheets Gradebook that automatically averaged and converted the score to a letter grade.  I also had to record scores in Infinite Campus.  I wasn't a fan of having to manage two separate gradebooks, but I survived.

Miscellanous Tasks (20% of Quarter Grade):

I did a lot of thinking about the types of assessments that I have used in past years and how they would fit into a target based grading system.  I wasn't ready to completely remove the variety of assessments that have been a staple in my classroom, so I decided to create a separate category and maintain the ability to assess students in a variety of ways.  The learning target average score counted as 80% of the quarter grade, while the "miscellaneous tasks" counted as 20% of the quarter grade.

One of my biggest concerns about implementing target based grading was that the assessments would become "silos" - too focused on one particular target.  I want students to see and understand the connections between the learning targets.

Some examples of assessments that went into this category included:

• In class group tasks
• Every couple of weeks, I have students work in pairs during class to solve review problems.  A majority of the problems relate to the geometric concepts and topics that we have learned about up to that point.  Some of the problems review middle school and algebra 1 topics; others focus on probability and statistics.  I pull a lot of questions from ACT reviews to expose students to those types of questions.  I also include problems that connect multiple learning targets together and/or include different solution methods.

• Choice Assignments
• To help try to increase student engagement in my high school, all teachers were asked to implement assignments where students had a choice of options.
• Desmos activities
• From time to time, I will assess a Desmos activity.  Typically, these activities are completed in class as part of the lesson for the day.  I will assess them when I want to ensure that students who were absent during class complete the activity.
• Projects
• Each quarter, students complete at least one project.  Some projects are in groups, others are individual.
• Reflection tasks
• I had students reflect on their learning with the help of Flipgrid.

• I also had students write an email each week to reflect on their learning.  The email went to their parents / guardians and to me.  Students would have to answer a series of prompts that helped guide their reflection.  See an example of my prompts here.

One thing that I removed from class this year was "Parent Tests".  In the past, I would send a multiple choice assessment home each unit for parents / guardians to complete.  The questions would relate to the concepts we were learning about in class.  There was a process that needed to be completed and students would earn extra credit if they completed the tasks and returned the paper.

I've learned that awarding extra credit - especially in way that involves a student's situation at home -  is an inequitable practice.  I have decided to not award any extra credit from this point forward.  I am in the process of researching ways to include parents / guardians in the learning process again.

Part III.  Implementation Details

I want to highlight and comment on a couple of things I learned during this first year of implementation.

I made three sets of each quiz.  Each set was intended to be equally difficult.  Students had the opportunity to take the quiz earlier that the designated quiz day.  Students taking the quiz early were given Set #1.  Set #2 was given to every student who took the quiz on the quiz day.  Set #3 was given to students who wanted to retake.  If a student needed a second retake, they would then take the quiz that they hadn't yet taken.


On the day following a quiz day, students would have "WIN" (what I need) time.  Students would get their graded quizzes back and do the following:

1. Write their reflection email (see above).
2. Begin the quiz correction process if they scored less than a 3.0.
3. Work on enrichment tasks if all scores were 3.0.

Some students would also use that time to work on quiz retakes from previous quizzes, assuming the retake deadline had not passed.

I would meet individually with each student to check in with how they were doing during this time.

Some students used the WIN time very effectively.  Students were able to ask questions of each other.  A lot of peer helping took place.

As the year went along, more and more students started abusing their time during WIN days.  I would see students working on assignments from other classes.  Others would treat the time as a social hangout.  I need to improve my classroom management a bit on those days moving forward.


Each class had its own tray on my desk for students to turning their work in.  This helped manage the steady flow of papers that were turned in each day.

Each student had their own hanging folder in a basket at the front of my room.  I would put all papers (graded quizzes, quiz correction forms, notes from class they missed, etc) in their basket.  It was their job to empty their basket as they entered the room each day.  Being able to "hand back" papers at any time was a huge time saver.

Speaking of grading papers... it was a daily job.  Each day, there was always something turned into the trays.  I felt the responsibility to grade papers and update grades every night.  If it was a quiz day, students needed their quizzes returned the following day for WIN time.  If it wasn't, students needed daily feedback on quiz correction forms and quiz retakes.  The process of retaking depended on it.

That said, in past years I would find myself grading every night as well - often times homework.  I felt much more motivated to grade quizzes, retakes, and quiz retake forms versus homework.  At minimum, I knew that the quizzes and quiz retakes were authentic evidence of what the students had learned.  I dreaded grading homework knowing that a certain percentage of students had copied their answers from someone else and learned nothing along the way.


One grading note:
I did have a few students average between a 1.75 and 2.00 on their target based assessments, which converted to a 64% in the learning target assessment (80%) category of the gradebook.  Their grade on the miscellaneous tasks (20%) was fairly good, so those students did pass the semester when the weighted grades were calculated.


Communication to parents / guardians about the grading system was important.  There were some parents who asked for clarity on the grading system at the start of the year.  I included a detailed explanation in one of my newsletters. 

I started the year with a quiz over the prerequisite skills.  The quiz didn't count towards the student's grade but I scored the quiz using the target based system.  It served as a good example for students to see how they were going to be assessed.


Part IV.  Reflection / Next Steps

I felt the target based system was effective in helping develop growth mindsets in students.  I liked that students didn't get their graded quizzes back and immediately saw a score / total points or a percentage.  Instead, they saw scores for each target.  In the case where a student didn't do very well on one or more targets on a quiz, it was still easy to shine positive light on the targets they did do well on.

I had to train myself to not be frustrated when students struggled on the first attempt on the quiz.  I had to remember that this was their first attempt at each quiz and that they did have the opportunity to retake.  I needed to focus on the final scores after the retake deadline had passed.  After all, those were the final scores that students were earning.

Opponents of a target based grading system have a worthy argument centered around that previous paragraph.  What's stopping a student from not studying / preparing at all for the first quiz when they know they always have an opportunity to retake?  What type of bad habits and lack of work ethic / preparation does that develop?

My counter to that argument lies in my belief that if we teach students to be mindful of their learner agency and the 16 Habits of Mind, students will begin to make make the correct decision when it comes to preparation and work ethic.  Yes, I believe that the mathematics I teach in geometry is important for students to have future success.  But teaching students to be lifelong learners and to possess a growth mindset and self confidence is more important. 


In the future, one long term change that I'm interested in looking into would be the idea of "mastery" learning.  A student would need to demonstrate mastery on each standard before they would be allowed to move on.  In other words, a student must earn a 3.0 on each learning target (or group of targets on a given quiz) before they move forward.  A big change in the structure of our class schedule would need to take place in order for this type of change to be implemented.  It is something our district is looking into pursuing and would help fight against students doing the bare minimum to pass.


I do welcome all feedback and discourse around this system in an effort to improve for future years.  I hope to convince my colleagues that target based grading is something we should be doing throughout our entire department. 

NCTM Conference @ Orlando Reflection

I’m on my way back home from the NCTM Regional Conference in Orlando.  I had an awesome four days in Florida.  My brain feels somewhere between the consistency of oatmeal and Jello.  I need to get my thoughts recorded before I return home to four children and the responsibilities of real life.  [Update: I didn’t get the full post written before I returned home; the movies on the airplane stole my attention.]

I had initially planned on doing a running diary-like blog post of my experiences at the conference, but soon realized that there is too much info to consume to be continually writing and reflecting.  Instead, I give you my five biggest takeaways from my conference experience.

1.         Desmos is still a mystery to too many classroom teachers.

            Okay, not all of Desmos.  But the teacher activities found at teacher.desmos.com.  In the first session I attended on Thursday, Matt Vaudrey (The Classroom Chef) had participants pair up with a partner and play Polygraph.  I rotated around to four different people and asked each of them if they had heard of Desmos before.  Three of out four responded along the lines of “Yeah, my students and I use the calculator quite often.”  When I asked them about every using Polygraph before, all three responded “No” and had never been to the Desmos teacher site.  The fourth person had never used Desmos at all before.

            Overall, I counted seven sessions (out of about 260) that included Desmos in the title or the description.  Other session may have absolutely used Desmos as part of their presentations and simply didn’t include “Desmos” in the description.  Not all of the seven sessions necessarily used the Desmos teacher site.  I’m by no means advocating for Desmos to take over the conference.  However, I continue to be floored at how many teachers have no idea that the Desmos teacher site exists.

            When talking to some of my Desmos Fellow / MTBoS colleagues, I mentioned my surprise at the lack of knowledge about the teacher site.  One conjecture we made is that if you visit desmos.com there is a link to the teacher site, but the link doesn’t really “stick out”.  We felt as though flashing neon lights might help.  Another conjecture is that until textbook companies direct teachers to go to the teacher site, it will never reach all who really need to see it.  I’m curious about something… textbook companies like Pearson and CPM are now starting to embed Desmos activities into their curriculum.  I’m wondering if teachers using those resources are prompted to “Go to teacher.desmos.com, create a class code, etc” or if they simply are able to run the activity via a link found in their curriculum’s resources.

            Teachers need to be told about the Desmos teacher site and need to be guided through setting up their account, searching for & bookmarking activities, creating a class code, and using the teacher dashboard.  There is also a strong need for a session where the Activity Builder is demonstrated, and the Activity Builder Code is investigated.  Which brings me to…

2.         I feel really motivated to share with other teachers by speaking at conferences.

            One NCTM regional conference next fall is in Kansas City, which is less than 6 hours away from Brookings via car.  The deadline for proposals to speak is December 2^nd.  I’m going to apply to speak and I’m leaning toward my proposal being about the Desmos teacher site.

            This week, I prepared a number of proposals for sessions at the SDCTM conference in February.  My colleague & fellow Desmos Fellow Jarrod and I are also going to submit a proposal for an in-depth session at the TIE conference in April.  I’m also happy to be presenting a full day session on Desmos at the SDCTM Summer Symposium in July.

            Also this week, I gained a lot of confidence in my ability to speak on ideas and things happening in my classroom that are not connected to Desmos.  Resources such as Which One Doesn’t Belong?, Estimation 180, 3 ACT tasks, My Favorite No, and Padlet had their fingerprints in many sessions.  Manipulatives such as Algebra Tiles, Patty Paper, and GeoBoards were demonstrated as tools that help student develop conceptual understanding.  I regularly use all of these things in my classroom.  One of the session proposals I prepared for the SDCTM conference demonstrates a few of these resources.

3.         I have fresh ideas about how to improve what I’m doing in my classroom.

            Continual improvement is something I like to think I strive for.  I gained a lot of new ideas this week on things I can do to improve my craft.  A couple of ideas I’m hoping to implement soon are warm-up routines, tweaking my WODB a bit to make students think about a reason each one doesn’t belong, and using GIFs embedded into Desmos to help students visualize the intended mathematics (thanks, Jedidiah!).  Also, I was reminded that I need to take a long look at Mathalicious and Quizlet Live; both resources seem to have some pretty strong supplementary resources.

4.         TI and I are on a break.

            This takeaway needs its own blog post.  Coming soon…

5.         The online math community is powerful.

            I’m going to have to say that networking & collaborating was one of the highlights of my week.  It began before the conference even started while I was walking to the Wednesday keynote session.  I bumped into Sam Shah on my walk to the conference center.  He and I met this summer in San Francisco at the Desmos Fellows weekend.  He introduced me to two of his colleagues who were walking with him.

            Then in the keynote session, I happen to sit next to Tracy Johnston Zager.  Her and I have a number of short conversations as part of the interactive session.  Directly in front of us are Desmos Fellows Heather Kohn and Lisa Bejarano.  Heather had asked Lisa and I to present on the Global Math Department’s webinar back on September 19^th.  (Our session was titled “What’s New at Desmos?” and yes, Dan Meyer presented with us.  Due to Dan’s loyal followers, there were over 500 people trying to view the webinar.  We crashed the host server & were unable to effectively show what was new at Desmos.)  Heather and Lisa introduced me to #MTBoS faithful Hedge and Joel Bezaire.  Michael Fenton was one of the keynote speakers and I spoke with him briefly after his presentation. 

            The next two days, I run into Desmos Fellows Carl Oliver and Jedidiah Butler.  I chatted with Christopher Danielson about this “Math on a Stick” at the Minnesota State Fair.  I sat next to Kyle Pearce in a couple of different sessions.  I met Justin Aion and David Wees.  I caught up with David Barnes and Patrick Vannebush, both of who I met at NCTM Minneapolis back in 2015.  The list goes on…

Holding down the fort at the #MTBoS booth.

I’d strongly recommend attending an NCTM if you have the resources to do so.  SO.  MUCH.  COLLABORATION.  I feel extremely fortunate to be able to attend.  I want to say “Thank You” once again to Daktronics for supporting SDCTM and the SD Math Teacher of the YearAward.  I'm keeping my fingers crossed that I'll be presenting next fall in Kansas City.  Time to get working on the speaker proposal!

GRIT...

This past Wednesday, our high school launched what we're calling "Advisory Period".  In brief, advisories will act a little like a homeroom for our high school students.  Once a week, students will meet with their advisory group for 30  minutes and engage in some sort of task -- team building, character building, class meetings, etc.  Advisory teachers will also monitor student grades and provide an extra layer of support for students who might be struggling.

Advisory groups will be grouped with students in the same grade.  I have been assigned students from the incoming freshmen class.  Therefore, this spring I was assigned to help the counselors with the entire class of seniors.  The counselors had a list of newsworthy items they disseminated to the seniors.  They also showed the seniors a video of a TED talk by Angela Lee Duckworth titled GRIT: The Power of Passion and Perseverance.

As I watched the video, I found myself inspired by Angela's explanation of "Grit".  She says, "Grit is passion and perseverance for very long-term goals.  Grit is having stamina.  Grit is sticking with your future, day in, day out, not just for the week, not just for the month, but for years, and working really hard to make that future a reality."  I started to reflect on my goals and dreams and arrived at the realization that I haven't been very gritty as of late.

In 2015, I was nominated for the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST).  I worked hard to complete the challenging application and later found out that I was a state finalist for the award.  Ultimately, I did not win the award.  I received feedback on my application from the state and national level reviewers.  Much of my application was strong, but not strong enough.

Due to being a state finalist, I was automatically eligible to re-apply in 2017. [2016 was a K-6 level year.]   Much of my previous application can be used again, but improving it is where I've lacked grittiness.  I haven't had the motivation or perseverance to dig in and improve it.  The application is due on May 1st and the clock is ticking.

Thank you, Angela, for the inspirational talk.  Not only am I going to complete the award application, you have also re-kindled my motivation to write blog posts and be more reflective in my practice.  Sometimes I need a reminder to work hard and think critically about my teaching style, pedagogy, and decisions.  Angela's talk served as a great reminder.

Better Questions

I know, I know.  Week 3 of the 2016 Blogging Initiative has long come and gone.  It's nearly the end of week 4!  I apologize for the tardiness.

I love the topic of "Better Questions" not only because the types of questions you ask can really dictate the type of classroom and style of teaching you have, but also because I need to continue to grow in the area of questioning.  Blogging about questioning will help me re-focus on the types of questions I'm asking my students.

This past fall, I presented a training module to HS / MS math teachers that focused on Effective Questioning.  The module brings to light the four levels of questions defined in NCTM's Principles to Actions (2014).

Question Type		Description
1	Gathering Information	Students recall facts, definitions, or procedures.
2	Probing Thinking	Students explain, elaborate, or clarify their thinking, including articulating the steps in solution methods or the completion of a task.
3	Making the Mathematics Visible	Students discuss mathematical structures and make connections among mathematical ideas and relationships.
4	Encouraging reflection and justification	Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work.

I've set the goal of asking more level 3 and 4 in my classroom, including on assessments.  These types of questions are sometimes tricky to create and grade.  Here is an example of a question that I asked my algebra 2 students.

I consider this a level 3 question due to asking students to make connections between the factors, solutions, and zeros on the graph.

Some example of student work:

Student 1: Excellent.

Student 2: This student did not understand the connection between the zeros of the graph and solutions of the equation.

Growth Mindset & the Smarter Balanced Assessment

I was first exposed to Carol Dweck's research on fixed and growth mindsets a few years ago when I was completing some of my graduate coursework.  For those of you who haven't heard about mindsets, you can find a lot of resources online (here and here to name a few).

Dweck's colleague, Jo Boaler, has completed some further research on mindsets and the implications in the classroom.   If you're really interested in learning about mindsets in a mathematics classroom, I would recommend taking Stanford's free online class (sign up here).

In Dweck's Self-Theories book, she discusses the reaction of students with a helpless mindset (fixed mindset) when they experience failure.  In short, when a student with a fixed mindset experiences failure they begin to fall into a helpless state of mind.  They quickly lose confidence in their abilities and lose perspective on the successes they had achieved in the past.  Moreover, many students who had fallen into the helpless mindset "abandoned or became incapable of deploying the effective strategies in their repertoire." (pg. 9)

After hearing that research, I grew concerned about students who have a fixed mindset and their ability to successfully complete the Smarter Balanced assessment.  The Smarter Balanced Assessment is a computer adaptive test.  Students are given grade-level questions for the first two-thirds of the test.  Then the computer software selects remaining one-third of the questions based on the student responses up to that point.  If a student is answering questions correctly, then the software can select questions from a higher grade level.  Conversely, if a student is answering questions incorrectly, then the software can select questions from a lower grade level.

Theoretically, this type of testing system makes sense.  It's designed to find the "boundary" of each students' achievement level.  My concern lies with the students with fixed mindsets.  For those students, the "boundary" is like an electric fence.  The test is designed for students to eventually touch the fence.  Once a student with a fixed mindset does touch it, the electrical current sends shocks throughout their body.  They lose ability to focus on the problems and are more focused on how much the fence shocked them.

Dweck summarizes her research by saying "...the helpless response is a reaction to failure that carries negative implications for the self and that impairs students' ability to use their minds effectively."  I fear the computer adaptive test could indirectly lead to major negative consequences for students with a fixed mindset.

What can we (teachers) do to help?

I think the best way to help combat this potential problem is to teach students about fixed and growth mindsets.  I am planning to introduce these ideas during the first week of school in all of my classes.  More to come as to what that will look like...



Dweck, Carol S. Self-theories: Their Role in Motivation, Personality, and Development. Philadelphia, PA: Psychology, 1999. Print.