More Accurate Self-Reflections

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Improving how students reflect on their math progress has been one of my goals during the past few years.  It’s a topic that I’ve been trying to incorporate more in the classroom. That reflection piece in my classroom has changed quite a bit since starting this journey.

Last year students would take an assessment, review their scores and then fill out a reflection sheet.  Students filled out the reflection sheet the best that they could.  The students and I would review the test and reflection sheet to determine the next steps.  Some reflections were spectacular and had a lot of insight, others didn’t. Most of the time the next steps included items like studying more before the test, reviewing a certain concept in more detail, practicing specific skills, or dedicating more time to the subject.  I’ll admit that too many of the nexts steps were vague and wouldn’t match the SMART criteria.  I was glad students were creating goals and following through.  Refinement was needed, but I appreciated that students were lifting up more responsibility for creating their math identities. The students did a fine job following up with the next steps, although this was inconsistently implemented.  I’d check-in on goals during the next reflection time.

While reading Make it Stick (I’m on the second renewal from the library), I found something that I’d like to keep in mind for the new year.  In chapter five the authors discuss the Dunning-Kruger effect.  Research has shown that people (students) sometimes overestimate their own competence.  They “… fail to sense a mismatch between their performance and what is desirable, [and] see no need to improve.”  As I continued reading I found that lower-performing students were the most “out of touch” in gauging how well they were doing compared to the standard.  After reading this I started to think about how students accurately reflect on their math progress.

Students are often asked to compare their work to the criteria for success.  The points/letter on the top of graded work is generally perceived in black and white.  Students either view themselves as doing great or poor.  There’s nothing in the middle.  I rarely have a student that says they had an average test.  This becomes even more evident when students complete the reflection and goal setting sheets.  I’ve had a number of instances where students can’t come up with a goal for themselves.  Through probing questions I’m generally able to help students create a goal that is worthwhile, but this doesn’t always happen.  I believe math confidence and adopted math identities play a role here.  The perception is stuck on the score and it’s challenging to move beyond that number.  Maybe it’s because students aren’t as familiar in gauging how they’re performing compared to the standard? I’ve used different methods to encourage students to look at skills compared to points and this has helped, albeit the success using the table has been inconsistent.

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The authors of book discussed an experiment where poor performers improved their judgement over time.  These students received training specifically on the test concepts before the assessment. That time spent improved their self-reflections and they were more in-line with reality.  Basically, the students are better able to show sound judgement during self-reflection if they understand the concepts.  Accurate self-reflection becomes an uphill battle if they don’t.

Moving forward I’d like to spend more time discussing error-analysis and misconceptions with the class.  When students are aware of how these specifically exist then they’re better able to analyze their performance.  Pre-loading that meta-cognition piece is something I want students to keep in mind during the self-reflection process.  I think it will deter students from making statements like “I don’t know what goal to make” or “I need to work on everything.”  These types of statements are disheartening.  I think having exemplars might help instead of just diving in and asking students to reflect.  Having a clearer direction and possibly having a reflection time that occurs more frequently could also help.  Math isn’t always perceived as a subject where students are asked to create some type of narrative and connect to the text/content. I find that students rise to the challenge when I give them an opportunities to do so.  I believe that giving students opportunities to analyze, reflect, and set goals for themselves will empower them to create more accurate math identities.

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Moving Away from the Gifted Math Label

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I’ve been paging through Jo Boaler’s Mathematical Mindsets lately.  I’m finding a few takeaways as I’ve been reading sections over the past few days.  My school has embraced some of the ideas in the book and we’ve been taking small steps each year.  One idea I found interesting relates to gifted students.  Page 94 discusses the “myth of mathematically gifted child.”  I feel like that statement is ripe with controversy as many are for or against the idea.  Most parents, teachers, and students have at some point in their life been told or shown their math identity.  Then that math identity may or may not be adopted and confirmed by the student. That communication can come from a teacher, parent, or somebody else.  Sometimes it comes from a single teacher or constant grades on assessments/assignments. Usually it’s developed early in life and continues with that individual.  People often can’t shake the generalization that they’re “good” or “terrible” at math.  I hear this at parent/teacher conferences, at school meetings and on EduTwitter.  Of course this is a generalization, but I find that this math stigma has lasting consequences.

I believe that the same stigma has the potential to occur with the “gifted” label.   I find that this can happen as early as the elementary level or even before then.  In an effort to address the needs of all students sometimes elementary schools group students by perceived math ability – emphasis on perceived. This often takes students and places them in different math classes during instructional blocks.  Students are moved to these different levels based on standardized test scores, classroom tests, teacher recommendations, or some other data that the team feels is necessary.  The groups can be fluid and change every unit, but sometimes they don’t. In some instances, school also have advanced math classes for students in upper elementary.  These classes might have a gifted label associated with them.   Although they’re labeled “gifted math” the roster doesn’t match the label.  The classroom rosters are often based on a criteria.  Sometimes the criteria is heavily weighted towards one single test-score cutoff, accounting for 40 or more percent.

Many questions come up regarding the actual percentage for students that are identified as gifted.  Most gifted specialists tend to agree that the amount is less than 10%.  Yet, these classes that are labeled as gifted tend to have 1/4 or even 1/3 of the total grade level population.  These classes may be accelerated, but not necessarily be meeting the needs of all the students that are identified.  Moreover, moving students to and from these classes can prove difficult as social/emotional consequences play out.  Often these classes aren’t as fluid and the roster doesn’t change as much since the students are accelerated from day one.

When shopping for school districts I sometimes find that parents are looking for whether schools have gifted classes for their child.  Schools might communicate on their website or through brochures that they have “gifted” classes, but in reality they’re accelerated subject-oriented classes.  Gifted students have academic and social/emotional needs and funding isn’t always available for this need.  It’s up to the local districts to create a system to meet the needs for these students.  I’m assuming positive intentions for the schools and districts in this scenario. In an effort to please the community and potential registrations, districts might used the term gifted to mean that the needs for high-achieveing students will be met.  Also, students that participate in these classes are artificially given the gifted label and they adopt the identity.  For some students they thrive in the class and it’s just what they need.  For others, it’s the opposite. Students struggle and feel contempt for math as they attempt to live up to the label of the class.  Having this happen at the elementary level sets the stage for a student’s math identity into middle school and beyond.

Labeling a class as gifted has consequences.  I want students to be able to create and maintain their own math identities.  Creating engaging math experiences for students with a heavy does of individual reflection can help students decide for themselves how they feel about math.  Regardless of their assigned math identity, I’m hoping my math class provides an appreciation, curiosity, and enthusiasm for mathematics.