Are We Teaching for Cognition or Compliance?

When my daughter was in 5th Grade, she brought home a worksheet that featured a series of multiplication problems she had to solve using this graphic.

I am an educator.  My experience has primarily been in teaching English and language arts at the middle and high school level.  However, I did a stint of middle school mathematics during my first year of teaching due to the school needing a math teacher and since I was the last hired ... well, you know how that goes.  While I don't consider myself to be a "math person", I have become skilled and proficient in mathematics mostly out of necessity and my own frustration with the concept.  However, I had never seen this graphic before.

When I showed this to my wife, who is an elementary teacher, she informed me that this is "one of those methods Khan Academy uses".  I went on Khan Academy's website and sure enough, there it was - the Lattice Box, the name of this foreign graphic my daughter brought home and was required to use to multiply multi-digit numbers.  I studied how to use the method and found it to be highly confusing, which surprised me because I am a visual learner but could not figure out how the pieces of this cube fit together.

I asked my daughter if she could just multiply the numbers using more conventional and traditional methods, and she said, "No, I have to do multiplication this way!"

I said, "Wait a minute.  What's more important here - that you understand what is multiplication and how and why it can be used to determine amount or that you use this method?"

She said, "Daddy, this is the way I have to do multiplication now."

That made this assignment much clearer to me - and also why there's such misconception and misinformation about this notion of "Common Core Math" and "Common Core English".

Interestingly, a week later after working on this assignment with my daughter (which we completed using the Lattice Box even though we both disliked the method), this story and the accompanying image was making the rounds on social media.

Perhaps some of you may remember this story about the father whose rant about the "Common Core Math" homework their child brought home became the viral sensation and caught the attention of magazines such as Time Magazine and even a featured spot on an episode of THE GLENN BECK SHOW.  The misinterpreted message became, "This is now how our children need to do math!"  No more could our children just borrow the one, regroup, perform long division, or use algorithmic formulas.  This was now the "New Math" our children needed to learn.

I became curious about what exactly what was this method students were now "required" to learn and use to subtract numbers, and I discovered through research and investigation that this graphic or tool featured in the homework assignment is  the empty number line, which is a model for addition and subtraction by researchers from the Netherlands in the 1980s.  I read about this methodology, how it was developed, and how it should be used, and it was fascinating.  I took one of my wife's elementary level math texts and worksheets and experimented with this methodology.  Sure enough, I attained the same differences I did when I subtracted using the more conventional and traditional method I was taught.  Still, I was fascinated to learn about the history and development of this tool and experience how it could be used.

After this experience, I decided to do some research and investigation into Lattice multiplication, and I found that Asian and European cultures have been using this strategy to multiply numbers as far back as the 13th Century.  I learned the history and development of the Lattice box and experimented with how it could be used to multiply multi-digit numbers.  Personally, I found the method to be confusing and even cumbersome, and I would not choose to use it.  However, again, I was fascinated by its history and development.

Both my daughter's homework and the Facebook father's viral posting piqued my interest to learn about the different methodologies that can be used not only to perform the four operations of arithmetic - addition, subtraction, multiplication, and division - but also help deepen conceptual and procedural understanding about mathematical practices, principles, and processes.  I learned that with math there is usually only one possible answer (which is what I already knew), but I discovered so many different methods and ways that the correct answer can be achieved and attained.  I did not find all of these methods and strategies and methods to be helpful or even useful, but I did enjoy experimenting with these practices and procedures and deciding which method would work best for me.

This experience reminded me of how I much I disliked not only instructing but also evaluating my students on how effectively they can use specific methodologies and strategies in English language arts.  I disliked teaching and grading my students on how to diagram sentences because I did not like using the method.

I also disliked requiring my students to use the Jane Schaeffer Writing Method because that was the writing program and process the district and school where I was working adopted.  While some of my students benefit from these methods, the majority of them did not, and I found myself frustrated teaching them not only because my students were struggling but I also struggled to use these methods and strategies that did not meet my learning style.  It actually caused me to have one of the worst teaching experiences in my career - and this was in an AP English Language class!  These kids hated writing style analyses for me not because they were frustrated in determining the tone and effect of the craft, structure, and language of the texts they were reading but because they had to use THE JANE SCHAEFER METHOD!  In fact, that became the name of the pain they felt from writing.

This is where teaching becomes a miserable experience for both the students and the teacher - when we are FORCED to use a prescriptive method, strategy, or technique to answer questions, address problems, and accomplish tasks.  We have to use THIS READING PROGRAM because that's what the school adopted.  We have to use THIS MATHEMATICAL PROCEDURE because that's what the district or charter has decided to use.  While these methods, strategies, and techniques are proven effective, they're not for everybody, and the mere mention of their names can cause both kids and adults to cringe.  Try it.  Mention Singapore Math or whole language and see the reaction and response you get.

Now we have a new name for our pain in education: Common Core.  "Common Core Math", "Common Core Reading", and "Common Core Writing" - the very name strike dread and disgust in the hears of many!  They are characterized to be as evile and vile as Darth Vader, The Joker, Freddy Krueger, or Hannibal Lecter.  Their names are spoked with a sneer or a tone of disdain and even fear and hatred  The parents and even the kids have said, "Can't we just use the old way to do math or read text?" and they are being told, "NO!  This is the way you must now read, write, and do math!"

According to whom?

I have reviewed the questions on the PARCC and SBAC exams extensively, and I have yet to see anything that resembles the practices and procedures provided in the textbooks, presented on the worksheets, or featured on Khan Academy.  I would presume this is not the intention of the textbook publishers or even Saul Khan.  However, the message has been grossly misinterpreted to state, "This is NOW HOW you must demonstrate and communicate your learning!"

So my question to consider is this - when we teach, are we teaching for cognition or compliance?  

Are we requiring students to answer questions correctly by following directions as explicitly and prescriptively as they are taught or are we encouraging them to think deeply and express and share how and why they can achieve and attain correct answers, desired outcomes, or specific results in different ways?

Are we challenging students students to think deeply and express and share how they could transfer and use what they are learning to answer a question, address a problem, or accomplish a task, or are we directing them to understand there is only one way to answer a question, solve a problem, and complete a task, and you must do it this certain way just as you were taught?

Perhaps you're saying, "But the curriculum features all these different methods and strategies the students must use to demonstrate and communicate deeper knowledge and thinking." True, but what if we approached these different methodologies, strategies, and techniques not as a mandated assignment they must complete but rather as a hands-on learning experience in which they experiment with using these practices and processes and decide whether they want to use this particular method or another strategy?  Would they not only become familiar with these different processes but also realize there may be more than one way to answer a question, address a problem, and accomplish a task and they have the freedom to choose the method that would work best given the circumstances, the context, or even their own personal preference?

If you truly want to understand how our children are expected to learn math and why they should experiment with these different methodologies, I recommend you watch this video by Dr. Raj Shah, who explains perfectly how we should teach math for cognition, not compliance: https://www.youtube.com/watch?v=X_CK1e0Lmxw

I ask you educators to consider when you send your students home with those homework sheets that feature the Lattice Box or the empty number line or require them to identify the parts of a sentence through diagramming or write an essay using the Jane Schaeffer writing method, are you teaching for cognition or compliance?

Erik M. Francis, M.Ed., M.S., is the lead professional education specialist and owner of Maverik Education LLC, providing professional development and consultation on teaching and learning for cognitive rigor. His book Now THAT'S a Good Question! How to Promote Cognitive Rigor Through Classroom Questioning will be published by ASCD in February 2016. For more information on this topic or how to receive professional development at your site, please visit www.maverikeducation.com.

How Authentic Are Your Assessments?

As our schools transition from implementing to evaluating instruction that addresses the cognitive rigor of college and career ready standards such as the Common Core State Standards, many states have decided to grant schools and students a reprieve from mandates that measure and monitor overall school performance based upon the results of the new state summative assessments such as the PARCC or SBAC.  Some state education agencies and charter school authority boards are allowing schools to use the site-based assessments they have implemented at their schools from testing corporations such as ATI-Galileo, NWEA, Acuity, and MAP for reporting student performance and progress.

However, how authentic are these assessments?  Are they expecting students to answer questions correctly based upon how effectively they can remember, understand, and use what they have learned or are they engaging students to express and share how they would use the education and experience - or expertise - they have acquired and developed to address and respond to the question?

Authentic assessments resemble reading and writing in the real world and in school (Hiebert, Valencia & Afflerbach, 1994; Wiggins, 1993).  These assessments generally challenge and engage students to demonstrate and communicate their deeper knowledge, understanding, and awareness using oral, written, creative, or technical expression. They also prompt students read, review, and respond to texts or comment upon and critique the ideas, incidents, individuals, and issues they are learning supported by relevant and sufficient evidence and valid reasoning.  They also encourage students to share and show what can they do or produce with the deeper and broader knowledge and thinking they have acquired and developed.

In other words, they resemble how students will address and respond to circumstances and situations not only academically but also personally, professionally, and socially throughout and beyond their formal K-12 education.  Think about it.  How are we "tested" in life or the depth and extent of our knowledge and thinking evaluated?  The only time we would be given a multiple choice test is for certification or licensure or unless we go on a game show like Who Wants to Be a Millionaire? (see my other blog entry on Let's Make a D.O.K.!) Our knowledge and thinking is "tested" and evaluated based upon how correctly, clearly, comprehensively, and creatively we can communicate our claims, conclusions, and contentions.

That's how we should be authentically assessing our students - based upon how their ability to communicate the knowledge and thinking they have acquired and developed through their education and experiences.

In education, authentic assessments are typically used in active learning experiences such as project-based and problem-based learning that prompt and encourage students to create, do, or produce something - a plan, a product, or a project - that reflects and represents how deeply and extensively they have learned the subjects and topics they are studying.  The assessment is generally based upon the quality of the project produced or the success of the student to come up with a solution.

However, even though project design and problem solving are active and authentic learning experiences, are the final products and solutions students produce truly or authentically mark and measure the level and depth of their learning?

Don't get me wrong!  Project-based and problem-based learning are excellent instructional methods and strategies that not only challenge but also engage students to demonstrate and communicate their learning in-depth, insightfully, and in their own unique way.  However, when it comes to assessment, most PBL experiences merely scratch the surface, focusing on what can you create, do, or produce without delving into how and why you created, did, or produced the project or solution.

That is true authentic assessment - evaluating not only how correctly but also clearly, comprehensively, and even creatively can students communicate their knowledge and thinking using oral, written, creative, or technical expression.

 It's how we are expected to answer questions, address problems, and accomplish tasks in the real world.  Think about it.  In our professional and personal lives, when we answer a question, address a problem, or accomplish a task, we're not just expected to "just do it".  We're also expected to delve deeper by expressing and sharing how and why we answered, addressed the problem, and and accomplished the task.  We need to defend, explain, justify, and support our actions and decisions.  We are also encouraged to pass on our education and experiences - or expertise - to others.

Authentic assessment is about communication and expression, not just activity, production, and design.   The quality of the response is determined based upon the following:

• Did the student answer the question, address the problem, or accomplish the task correctly, clearly, comprehensively, and even creatively?
• Did the student express and share their claims, conclusions, and contentions in-depth, in detail, insightfully, and inimitably?
• Did the student strengthen and support their responses with textual evidence, personal experience, recorded observations, or scientifically-based research?

So how does this translate into the classroom?  We need to move away from tests that use multiple choice and provide assessments that utilize open-ended questions that provide students the opportunity to express and share the depth and extent of their learning.  We need to refocus our evaluation of student learning from determining whether students can answer the question correctly to whether students to defend and support their response to what the question is addressing using their education and experience - or expertise - as evidentiary support.  

However, this does not involve having students demonstrate and communicate their learning primarily through PBL experiences.  We can convert the performance objectives of college and career ready standards into good overarching and topical essential questions they can address and respond using the texts and topics they are reading and reviewing as evidentiary support.

Good overarching questions are the inquiries students will examine and explore throughout and beyond their K-12 education.  They address the core ideas and enduring understandings of an academic area, discipline, or field of study.  These core ideas are addressed in the disciplinary core standards of the college and career ready standards.  We can use the performance objectives to develop good overarching questions that can serve as the formative and summative assessments for a grade level or subject area.

Take a look at the questions in the accompanying graphic.  These are derived directly from the ELA / Literacy CCSS Anchor Standards for reading.  These are the good questions students will examine and explore throughout and beyond their K-12 experience with reading.  Consider how these good questions can act as the final assessment at a particular grade level or subject area.  They can also serve as benchmark assessments that progressively measure and monitor how deeply and extensively students have learned these concepts and content throughout their K-12 education.   Think about it.  What if students were asked these same questions at the end of every school year starting in Kindergarten and through 12th grade and used the texts and topics they read and review in class that particular as their evidentiary support for their responses?  How could this serve as a true measure of how deeply and extensively students have learned these disciplinary core ideas in a particular subject area?

The performance objectives for grade level academic would serve as the topical essential question for a particular unit or lesson. Take a look at the good questions that are derived from the performance objectives of the following math standards for a 3rd grade unit on multiplication and division. The cluster serves as the topical essential question that sets the instructional focus and serves as the summative assessment for the unit.  The performance objectives listed under the cluster serve as the daily good question that sets the instructional focus and serves as the summative assessment for individual lessons or learning experiences.  The problems students will be presented as part of the unit will serve as the textual evidence that strengthens and supports their responses.  We can provide a learning experience that challenges and prompts students to address and respond to one of these questions and use the problems they are presented to examine and solve as their evidence.  Look at the accompanying graphic that would drive a lesson on understanding and applying the Pythagorean Theorem.  The question students need to address and respond is the one in green at the top of the graphic.  The problems they need to examine and solve will serve as their examples and evidence that will strengthen and support their response to the question at the header of the slide.  However, I would advise not having the students examine and solve all these problems in one setting.  Ask them to address and respond to the good topical question and pick one or two problems to examine and solve to support their response.  The next day, ask them to pick two or three more of these math problems and explain how they can be solved using the Pythagorean Theorem.  At the end of the unit, present that topical essential question as the assessment or "test" question and have them pick the one problem they left remaining to strengthen and support their response.  It's practically a given that the one problem students' chose not to solve is the one they perceived to be the "hardest" one.  Think about how much you would build a student's confidence if they were successfully able to express and share how they could use the math to solve that problem they perceived to be so hard.  Also, consider how you would be able to assess their learning authentically by observing how deeply and successfully they can express and share how they can "use the math" - or rather, think mathematically. 

In English language arts, the overarching essential questions are the grade level performance objectives of the academic standards that will set the instructional focus and serve as the summative assessment for the course.  The topical questions will directly address the text or topic being read in reviewed in class.  Look at the topical essential questions for this book study on Charlotte's Web by E.B. White.  These questions authentically assess how deeply and extensively students understand the ideas and information presented in the text by challenging them to express and share what they have learned using oral, written, creative, or technical expression.  They will use specific evidence from the text to strengthen and support their responses. Similarly, these topical essential questions for a unit on Shakespearean tragic hero also set the instructional focus and serve as the summative authentic assessment that measures and monitors how deeply and extensively the students understand the texts and topics they are reading and reviewing.

To create authentic assessments that measure and monitor the depth and extent of students' understanding of the core ideas of an academic area, discipline, or field of study, look at the performance objectives of the disciplinary anchor standards and practices for a particular subject area.  You can use the ELA/Literacy CCSS Anchor Standards for Reading, the CCSS Standards for Mathematical Practices, the Crosscutting Concepts of the Next Generation Science Standards, or the Historical Thinking Standards, or the conceptual standards of the C3 State Standards for Social Studies.  Convert those performance objectives into good questions that ask students to address and respond how or why.

To create authentic assessments that assess and evaluate deeper and extensive knowledge and thinking about a particular text or topic, look at the performance objectives of the grade level or subject area academic standards that students will address as part of a lesson or unit.  Other than the English language arts college and career ready standards, these performance objectives generally challenge and engage students to demonstrate and communicate deeper and extensive content understanding.  The topical essential question will serve as the single question students will continuously examine and explain over the course of the unit.  It will also be the single question which students will need to address and respond at the end of the unit.  They will need to address and respond to this question by demonstrating and communicating their learning by processing the information they have acquired and gathered into their personal or self-knowledge and use specific evidence from the texts and topics they are reading, reviewing, and responding to as support.

That's authentic learning - expressing and sharing depth and extent of knowledge and thinking supported by examples and evidence - and that's what it means to assess learning authentically. 

Erik M. Francis, M.Ed., M.S., is the lead professional education specialist and owner of Maverik Education LLC, providing professional development and consultation on teaching and learning for cognitive rigor. His book Now THAT'S a Good Question! How to Promote Cognitive Rigor Through Classroom Questioning will be published by ASCD in February 2016. For more information on this topic or how to receive professional development at your site, please visit www.maverikeducation.com.

Burn This! Why the D.O.K. Wheel Does NOT Address Depth of Knowledge

How many of you have seen this graphic?

Perhaps you were provided this graphic from your district or school to use as a frame of reference for planning instruction and assessment for depth of knowledge.

Perhaps this is the image that popped up when you conducted an online search about depth of knowledge.

Perhaps some of you are using this to develop lessons and units that you believe prompt and encourage students to demonstrate their depth of knowledge about the concepts and content they are learning.

Well, stop it!  Do not use this wheel!  In fact, BURN THIS if not physically then out of your memory because this is NOT depth of knowledge.  It's actually a (very poor) graphic for demonstrating higher order thinking.

What's the difference?

Higher order thinking correlates to the kind of knowledge and type of thinking that needs to be demonstrated in order to answer a question, address a problem, or accomplish a task.  When we  plan instruction and and assessment for higher order thinking, we educators typically mark and measure the level of thinking students are to demonstrate using Bloom's Taxonomy - specifically, the revised version by Anderson and Krathwohl.

Depth of knowledge is an entirely different means of measuring and monitoring rigorous learning.  It correlates more to how extensively students are to express and share their knowledge and thinking.  In other words, are students expected to express and share depth of factual and conceptual knowledge (What is the information that needs to be known and understood?), procedural knowledge ( How can the information be used to answer questions, address problems, and accomplish tasks accurately and appropriately?), strategic knowledge (Why can the information be used to produced a correct answer, desired outcome, or specific result?), and extended knowledge (What else can be done with the information and how else could it be used?).  Webb's Depth-of-Knowledge model is typically used to designate the extent students are to express and share their learning.

Unfortunately, depth of knowledge has been misinterpreted and incorrectly perceived as being similar to higher order thinking, and much of that misconception can be contributed to the D.O.K. Wheel.  If you look at the different pies in the wheel, you will notice that it categorizes depth of knowledge by the actions students will perform.

That's higher order thinking, and those verbs are cognitive actions or processes students will demonstrate.  Depth of knowledge deals with the setting, scenario, or situation in which thinking is demonstrated.  It addresses context rather than cognition -- in other words, it's not what the student is expected to do or demonstrate but rather the scenario or the situation in which students express and share their learning.

A D.O.K.-1 assignment or assessment is very content-driven, focusing recognizing, researching, and rephrasing who, what, where, when, and how about data, definitions, details, facts, figures, ideas, information, principles, and procedures.  The intent of D.O.K.-1 experiences is knowledge acquisition - acquiring and gathering the information students will need to strengthen and support their thinking.  These questions, problems, and tasks  would directly address and respond to the specific texts and topics being read and reviewed in class.  For example, the work of literary fiction current being read, the mathematical concept being taught, the scientific subject, or the historical topic.  Students can think deeply about the concepts and content; however, the context is more academic and factual.

A D.O.K-2 assignment or assessment is highly procedural, challenging students to understand, analyze, and evaluate how does it function, how does it work, or how is it used.  The goal of D.O.K.-2 experiences is knowledge application - demonstrating and communicating how information can be used to achieve or attain a certain answer, outcome, or result.  These learning activities prompt students to answer questions, address problems, and accomplish tasks correctly and successfully by applying practices, principles, and processes accurately and appropriately.   Examples of D.O.K.-2 items and tasks would be to use a mathematical procedure to solve mathematical and real world  algorithmic and word problems, explain how a natural event of phenomena occurs, describe how a text or author expresses and shares ideas and information, or how a historical event turned out as it did.  

A D.O.K.-3 assignment or assessment engages students to think strategically and use reasoning to analyze and evaluate what are the causes, connections, and consequences.  The purpose of D.O.K.-3 experiences is knowledge analysis - examining and explaining why is this information essential and relevant to know, understand, and be aware of in order to study phenomena, solve problems, and solifdify meaning.  These learning activities prompt students to express and share why can the knowledge be used to produce a certain result and how can the knowledge be used to categorize, classify, and clarify ideas, incidents, individuals, and issues.  Examples would be analyzing why an author chose to present ideas and information in a certain medium and evaluate what is the effect the author's choices has on the text and the reader.  In math and science, a D.O.K.-3 question, problem, or task engages a student to a combination of deductive and inductive reasoning to examine and explain outcomes and results.  In history, students are engaged to establish historical arguments about the claims and conclusions made about historical ideas, incidents, individuals, and issues.  They also encourage students to think hypothetically about what if, what would happen, or what could happen given certain criteria or factors.

A D.O.K.-4 assignment or assessment encourages students to expand their knowledge and extend their thinking beyond the topic, the teacher, the text, and even themselves to consider what else or how else.  The intent of D.O.K.-4 experiences is knowledge augmentation and transfer - recognizing and realizing how and why information is beneficial addressing and responding to circumstances, issues, problems, and situations in a variety of circumstances and contexts.  These are the items and tasks that generally foster and promote active learning such as project-based and problem-based learning that encourage students to analyze and evaluate what impact or influence do ideas, incidents, individuals, and issues have across the curriculum and beyond the classroom.  They also encourage students to think creatively about what can you create, do, or produce with the deeper thinking and extensive knowledge they have acquired and developed.

Notice how these levels are categorized not by the cognitive actions the students are to take but rather the context in which students demonstrate and communicate their thinking.   While the level of thinking varies, the depth of knowledge depends upon the extent in which student are to demonstrate and communicate what they have learned - academically (D.O.K.-1), procedurally (D.O.K.-2), strategically and reasonably (D.O.K.-3), or extensively and authentically (D.O.K.-4).

Still, many of us educators and our students need some kind of graphic or visual to help us clearly "see the picture" presented by depth of knowledge.  The D.O.K. Wheel unfortunately brings more confusion than clarity.  Therefore, I would like to present a visual that could provide some guidance and support - the D.O.K. Ceilings.

This is the graphic I use when I conduct my presentations on questioning for cognitive rigor, which is defined by the level of thinking and depth of knowledge students are challenged and engaged to demonstrate and communicate in their learning.  Look closely at how this image is constructed.  These are not steps but rather ceilings that indicate how extensively students are to engage with the subjects and topics they are learning.  

Hopefully, this graphic will help you design those D.O.K. lessons you are desperately trying to develop and your administrators are wanting to see - and finally rid us of the grossly inaccurate D.O.K. Wheel.