Sunday, January 30, 2011

Standards Based Grading meets Marzano

Robert Marzano has been reviewing education research for decades and summarised his findings in a practical and concise teacher guide "The Art and Science of Teaching". (Marzano, 2007). So let's put our Standard Based Grading [SBG] hat on, and consider the key ideas from Marzano's first chapter, which asks the question:  "What will I do to establish and communicate learning goals, track student progress and celebrate success?"

The following ideas read almost straight out of the SBG credo:

Distinguish between learning goals and learning activities : It's important not to confuse learning goals with learning activities. A learning goal typically is stated in the form "Students will understand ____________ and be able to ____________".   Following Marzano, it is best practice to build our SBG standards on goals - not activities.  (Action Step#1, p. 17)

Write a rubric or scale for each learning goal: Marzano recommends a finely grained scale be defined for each learning goal. While he says a simple one is sufficient, which appears to be the way most SBG teachers are working, a finely grained scale provides more value. I'm not sure though if this is feasible when there are many standards for a topic - it may well overload the student and the teacher. (Action Step#2, p.19)

Assess students using a formative approach: Don't wait until the end of the unit - assess as you go. Yep - that's SBG. (Action Step#4, p.24)

Have students chart their progress on each learning goal: Well if this doesn't just scream SBG at you, I don't know what does. Marzano emphasises the importance of students evaluating their progress on each goal, as well as setting achievement targets and strategies. An implied caution for teachers using automated software for their SBG tracking is to ensure students engage with the data in a meaningful way - there is a risk the student could just look at a pre-generated graph and move on.  Marzano provides a proforma how a student can extend their chart into an active learning plan. (Action Step#5, p25)

Recognise and celebrate growth: Use the feedback about progress in SBG goals to show student growth - not just absolute achievements. (Action Step#6)

Marzano also offers a suggestion which can be used to extend SBG:

Have students identify their own learning goals: I love this idea! Extend the standards to allow each student to set an additional personal learning goal for what interests them, or what they would like to achieve for the current topic. While tracking student progress for their unique goal may add complexity, it seems like a valuable idea. A suggestion for those using Active Grade or some other automated system (Excel anyone?): make a standard called "Student Selected Standard" which can be marked off for all students - then a separate table somewhere to record what those selections were and how the student and teacher agreed it would be assessed. What a powerful meta-cognitive strategy(Action Step#3, p.23) 

All up - SBG as currently formulated matches 5 out of 6 of Marzano's recommendations in his first chapter, indeed Action Step#5 is arguably a prescription for SBG. Marzano is highly influential in the US education scene (and beyond) - so if people are asking you "Why are you doing SBG? Where is your evidence?" point them at Marzano's work and make the links to SBG. (Bonus: Amazon has the book on sale for $10.11!)

In concluding this tour of four different approaches to effective teaching, it is remarkable to observe all four approaches recommend similar, or at least complementary, strategies - many of which are at the core of the SBG idea. The Circle of Courage shows how SBG can contribute to psychosocial growth through mastery and independence, while providing opportunities to develop a sense of belonging and to practice generosity. Andrew Martin's work shows us how SBG can help build academic resilience and combat fear of failure by demonstrating to students how effort, strategy and attitude are the basis for improved performance and mastery. John Hattie's Visible Learning shows how the feedback provided by SBG can be used as a powerful tool for improving teaching practice - that SBG is as much a tool for transforming teaching as it is for transforming learning. And finally, Marzano reaffirms we are on the right track, and suggests extending our standards to include student selected standards.

A closing thought from Marzano about evidence:
It is certainly true that research provides us with a guidance as to the nature of effective teaching, and yet I strongly believe that there is not (nor will there ever be) a formula for effective teaching. [...] The best research can do is tell us which strategies have a good chance (i.e. high probability) of working well with students. Individual classroom teachers must determine which strategies to employ with the right students at the right time. In effect, a good part of effective teaching is an art. (pp. 4-5)

Where is the evidence for SBG? All around us!

Wednesday, January 26, 2011

Standard Based Grading : Show me the evidence!

One of my university tutors, Dr Nigel Goodwin, would regularly have us recite a catechism whenever we discussed ideas in education:
Show me the evidence!
And what is our currency for measuring the evidence? [yell it!]... 
Improved student outcomes! 
Forget the talk, the opinions, the fads: show me the evidence of improved student outcome. Careful though -  this does not mean just using standardised test scores based on the 3R's! We mean peer-reviewed evidence that we can have confidence in.

In looking for evidence relating to SBG as currently formulated and being trialled by science and maths teachers, part of the challenge is the newness of this formulation. So as a proxy for evidence about SBG, I'm looking at evidence of effective teaching practice and seeing if there are connections to SBG.  And when it comes to evidence, there is a special place in evidence heaven for John Hattie.

Hattie is famous for his meta-analyses - a technique that allowed him to review student outcome data for 80 million students, as reported in 50,000 peer reviewed studies. Using the concept of effect size, Hattie produced a list to answer the question ‘What has the greatest influence on student learning?'. Even more helpful than just presenting data, in his book Visible Learning (Hattie, 2009) synthesises these results into an explanatory theory.

John Hattie's Visible Learning in a nutshell:
Visible teaching and learning occurs when learning is the explicit goal, when it is appropriately challenging, when the teacher and student both seek to ascertain whether and to what degree the challenging goal is attained, when there is deliberate practice aimed at attaining mastery of the goal, when there is feedback given and sought, when there are active, passionate and engaging people (teacher, student, peers) participating in the act of learning. It is teachers seeing learning through the eyes of students, and students seeing teaching as the key to their ongoing learning. The remarkable feature of the evidence is that the biggest effects on student learning occur when teachers become learners of their own teaching, and when students becomes their own teachers. When students become their own teachers they exhibit the self-regulatory attributes that seem most desirable for learning (self-monitoring, self-evaluation, self-assessment, self-teaching). (Hattie, 2009, p22)
How does this relate to SBG? And how might it suggest we extend our thinking about SBG? Some of the more obvious connections are worth stating:

Explicit goals: SBG is all about explicit goals.

Appropriately challenging goals: SBG allows teachers and students to decide - based on previous results and current  intentions, what an appropriate goal for each standard is. They aren't pie-in-the-sky goals, they don't relate to abstract numerical grades - they are focused "I would like to get Proficient in "Can factorise a quadratic"" - and they allow us to agree that perhaps this student should aim for Expert, not Proficient.

Deliberate practice ... : SBG allows us to make the link between focused effort and mastery. A caution we need to bear in mind with SBG is that by allowing students to sense "I'm done - I've mastered that skill" - we may undermine deliberate practice. Is this any riskier than traditional grading practices? Probably not - but it's something to consider. How can we use our new SBG tool to encourage ongoing, deliberate practice?

... focused on mastery learning :  Yep - that's SBG!

Feedback is given and sought : The major strength of SBG. As we implement SBG, it's important we encourage students to actively engage with the feedback provided by SBG. (Effect size: 0.73 - 1,287 studies).  And even more importantly, that we respond to the feedback. Hattie writes
 "it is only when I discovered that feedback was most powerful when it is from student to teacher that I started to understand it better. When teachers seek ... feedback from students as to what students know, what they understand, where they make errors ... then teaching and learning can be synchronised and powerful. Feedback to teachers makes learning visible" (p.173).
So the most powerful feature of SBG may well relate to Hattie's observation that the biggest effects on student learning occur "when teachers become learners of their own teaching" (p.22)  In other words - if we have the perspective that SBG is a tool that allows us to continuously evaluate to our teaching - we transform SBG from just being another grading system into a powerful tool for monitoring and adapting our teaching.

So rather than "Hmm.. Johnny still hasn't reach proficiency on 'solving right triangles for the hypotenuse - what can he do?" we say "Hmm.. I taught this concept to Johnny for three lessons - what can I change?". And that's where the money comes in!

With apologies to "Jerry Maguire"
Next in this series: looking at the work of Robert Marzano. The evidence considered in this post relates to student outcomes - for an SBG perspective on student motivation and engagement see the earlier post looking at the work of Andrew Martin.   SBG is also considered in relation to a developmental framework called The Circle of Courage.

Saturday, January 22, 2011

Standard Based Grading : helping eliminate academic fear and failure

Following from the discussion SBG and the Circle of Courage,  I would like to consider SBG in relation to the work of Andrew Martin - a leading education psychology  researcher on student motivation and engagement.   Here's my interpretation in stick figures (with apologies!!) of Andrew Martin's most recent book Building Classroom Success: eliminating academic fear and failure.  While the book doesn't have stick figures, it's extremely well written and a great asset for teachers.

Students build a view of themselves that works like this:

As a consequence, students build many clever but often maladaptive behavours to protect their self-esteem. So for example: I only got 20% because last night I was playing games on the internet instead of studying - but really I could do it if I wanted to - it's not about my competence. In fact, the student is terrified they will fail, and so to protect their self-esteem, they make sure they play that game all night. We need to help students break the tight linkage they make between performance, competence and self esteem:

and instead help students see the role that effort, strategy and attitude play:

Observe also that knowledge and skills are identified as distinct from competence. They are developed through effort, strategy and attitude - and these are all factors the student can control.  We then extend the view to show that failure is not a direct link to competence; that competence can be developed; and that self-esteem can be built on more than just competence:

Andrew Martin goes on to encourage us to help students focus on mastery of the subject, rather than dwelling on performance compared to other students, and to show how effort, strategy and attitude will help gain mastery. Most importantly: to show students that these factors are actually under their control.

So where does Standards Based Grading [SBG] fit in this model?  Let me count the ways ... here are just a few:

Most importantly, SBG smashes the simplistic correlation of performance to competence. Instead of providing a single figure "you passed, you failed" therefore "you are smart, you are not smart", it highlights individual elements of knowledge and skills the student has mastered and has not mastered.  So long as we have the discussion carefully, we never impune the student's competence: we have a discussion about what they know, not how smart they are.  And note this works for the advanced student as well as the less successful student: they don't get "87% great!", they get "you understood this, now lets focus on these...".

SBG helps show students that performance depends on prior mastery : Academic success doesn't just happen because you are smart - it's built on successfully mastering earlier work. SBG makes this very clear - because mastery of previous knowledge is explicitly recorded and tracked.

SBG helps turn failure into feedback for future growth : When students encounter failure in assessment, big or small, they get specific information on where and how they might improve.

SBG provides a mechanism for having the discussion about effort, strategy and attitude : A concept that has come through strongly in the SBG discussion is that before students can ask to be reassessed on a standard, they have to actually do something to help master it, and demonstrate this effort, before we offer them the choice for reassessment.

SBG allows us to customise appropriate success goals for each student: For each student we can help them define mastery goals to extend them from where they currently are. We can also help them track improvement and personal bests, building their self-esteem in the process.

The take home message? SBG as it's being discussed in the blogsphere seems well aligned to best practices recommended by leading ed psych research for maximising academic success. Andrew Martin's work suggests we need extend the SBG process to look carefully at the "what happens next?" question: once we have determined where the student is at for each skill on the SBG chart, what sort of discussion do we have with the student? What can we do to support increased effort, appropriate strategy and positive attitude as the student prepares to either reassess a standard, or move to the next set of standards?  It seems we need to think carefully with the student which of these elements will benefit from further attention - and then help them find ways to progress.

Friday, January 21, 2011

So what happens in the first week of maths class?

With the new school year in Australia rapidly approaching, and for me, my first year as a teacher, I've been considering just what we need to do in the first week. Every new teacher is told it's crucial to get things right, at the beginning - there is no second chance. Assembling ideas from my training and, most importantly, from many experienced teacher friends, I've put together a list of what I believe are 27 (!) distinct elements I need to cover with my students. You may be surprised just how few of these elements relate to actually learning maths.

The challenge of course is to program these elements without overwhelming the students (and the teacher) - and all the while helping build an atmosphere of trust, community and motivation to learn. I'll follow up in a few weeks with some feedback on what worked and what didn't.

A big thank you to the many maths teachers on the NSW Department of Education Yammer network who offered ideas and helped me work this out. Check out Maths Links if you're looking for topic related videos recommended by maths teachers.

Monday, January 17, 2011

Standards Based Grading and the Circle of Courage

There's a movement growing in the edu blogsphere called Standards Based Grading [SBG, twitter #SBAR]. If you're not familiar with it yet - Think Thank Thunk's posts are a great starting place. In this posting, and the next few to follow, I would like to show connections between SBG and some of the educational ideas that have inspired and influenced me. But first - what is SBG?

SBG in a nutshell: Instead of doing a test at the end of each topic and giving a student a mark for the whole test, dissect the topic into individual concepts and skills ("standards"), and then, over time - during the teaching of the topic - assess competence in each discrete standard using a simple scale such as "developing, developed, mastered". Make the process visible to students, and give them opportunities to be re-evaluated on standards - with the proviso they can show they did something toward getting a better result. At the end of the topic, the overall student grade is derived by aggregating their current level of achievement on each standard. The goal is to have meaningful formative assessment that supports an ongoing learning conversation with students, providing visible and timely feedback to students and teachers.  (I think I got it all?)

SBG resonates with a model of student psycho-social needs which I find insightful and practical: the Circle of Courage, developed by Dr. Larry Brendtro, Dr. Martin Brokenleg, and Dr. Steve Van Bockern, derived from Native American concepts. They argue that young people, indeed all people, have needs in four key areas:  Belonging, Mastery, Independence and Generosity.

 Circle of Courage medicine wheel by Lakota artist George Blue Bird
via Reclaiming Youth International - poster available for purchase'

So where does SGB fit in with the Circle of Courage?
  • Belonging: We have the opportunity to present SBG as a class journey through the topic - a development of the whole class - to which we all belong. By allowing  students to be reassessed, we are telling students that even if they did not achieve mastery of a subject, they will get another go - they are still in the class, still part of the effort - they haven't been left behind!
  • Mastery: is the most obvious factor that SGB caters for: we emphasise student mastery of skills and concepts. It's not a number, a score we are aiming for - it's a specific mastery.
  • Independence: I love SBG for this: we offer students choices - choices to try again, choice as to which skills to try again, choices as to when they are ready for reassessment (within reason!)
  • Generosity:  SBG offers a unique opportunity for generosity. Once you have identified which students have mastery of a standard, make them the teachers for this standard - provide them the chance to be generous to other students by helping others learn how to master the standard.  Form students into small groups, assigning an 'expert' to each group - and have them lead the group in an activity.  You will be staggered at the student response - from both the experts and the developing students - and the research evidence is very clear on benefits of peer learning - for both the teacher and the learner.  Students really do seem to learn so much better from their peers. And unexpected things happen too: once one of my expert students - who was normally very talkative to the point of disruption, started telling off his students for talking too much and not listening. Priceless.
In the next few posts, I'll be exploring how SBG fits in with Andrew Martin's work on student motivation and engagement and John Hattie's Visible Learning.

Update Jan 22, 2011: This series continues with Standards Based Grading: helping eliminate academic fear and failure

Saturday, January 15, 2011

Inspiration from Bronowski's Ascent of Man

The best ever Christmas present: the full set of Jacob Bronowksi's staggering 1973 BBC series "The Ascent of Man" - a triumphant presentation of science, mathematics and art, delivered with warmth and style by an amazing human being. Unlike some other contemporary BBC series, this series remains fresh and exciting. The only slightly jarring element is the repeated use of "man" rather than "people" - but that's an artifact of the age. 
Jacob Bronwski on the island of Samos, exploring right triangles.
In Episode 5, "The Music of the Spheres", Bronowski reveals the mathematical elephant in its full glory. There is enough material in this one episode to last a full high school mathematics curriculum. I'm hoping my students this year will take some pleasure in watching some of extracts of this episode - we shall see! At the end of this post is a breakdown of the content. If you don't own the DVD, many extracts are available on YouTube.  Here is a wonderful segment on Pythagoras which could easily be extended into a student activity - either using physical media, or with software.

Topics Bronowski covers in Episode 5
with duration and suggested school grade level (using NSW syllabus)

Chapter 1: Pythagoras discovers mathematical relationships of notes of vibrating strings  (7 mins - maths starts at 4 min mark; Year 7/8)
Chapter 2: The nature of right triangles - reflection, rotation and Pythagoras' Theorem (7 mins; Year 8)
Chapter 3: Ptolemy - astronomy and geometry (4 mins; Year 8)
Chapter 4: Rise of Islam and flourishing of mathematics in the middle east (6 mins; Year 8)
Chapter 5: Tesselations at the Alhambra - good exposition of rotations and symmetry (8 mins; Year 7/8)
Chapter 6: Crystals forms - geometric structures in nature - related to symmetry (3 mins; Year 7/8/9)
Chapter 7: East meets West at Toledo: Arabic mathematics and astronomy arrives in Europe (6 mins)
Chapter 8: Geometric perspective (some nudity),  the dimension of time, Kepler orbits, calculus mentioned (8 mins; Year 10)

There is a significant amount of positive coverage of Middle Eastern culture in this episode, which should resonate with some student demographics who might otherwise feel mathematics is always about the Western World. 

Friday, January 7, 2011

Hanging on the Hills Hoist

It's a typical scene across inner Sydney the week after Christmas: friends and family out in the back garden, the BBQ is fired up, the adults enjoying a wine or three, resuming the perennial Sydney conversations about real estate, the shambles of state politics, what the kids are doing, plans for getting them into the school of our choice - debating the merits of public versus private schooling.  Meanwhile the kids are running around on the lawn, resuming their own perennial conversation between parents and children about the real purpose of the Hills Hoist: is it a utalitarian clothes dryer or a fantasy fairground carousel?

While we were debating whether Grade 4 children should be doing maths homework, I noticed out of the corner of my eye that the kids had progressed from just spinning around on the Hills Hoist to playing with the laundry pegs - they had begun to make chains of pegs, hanging from the line, linking peg to peg in single file. Maths homework indeed I thought, quietly to myself, and on a hunch I snuck away from the adults to join the kids.  It took some effort to hold myself back and not just take over the peg game (so much fun!) - instead I not-so-innocently asked the kids if perhaps the peg chain might be interesting if we tried branching it off by using the pegs slightly differently. We worked out how to clip two pegs at the end of one peg to create a fork - and then I pulled back to watch the fun. The kids proceeded for the next 30 minutes to build increasingly more complex chains, to transform them from straight lines to curved lines, branching them off, linking separate chains together.

Peg chains on the Hills Hoist - with Anya and Dom. (c) All rights reserved.
As the chains become more complex and longer, they started to break. One six year old child started comparing the different types of pegs we had, developed his own well reasoned theory about which pegs we should use and how. I laughed when I realised his boisterous smashing of other children's peg chains was a totally rational consequence of his theory - chains that did not conform to his design had to be removed!

I could not help but wonder, for children still at primary (elementary) school - would a thirty minute play session exploring shape and network connections using pegs on a Hills Hoist be as helpful as being made to sit at a desk at home and do maths homework? Hattie's meta-analysis found a negligible 0.15 effect size for primary students doing homework - so maybe there is something in this suggestion.