Category Archives: student-centered learning

Voice, Choice, and Ownership in PBL

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Have you considered doing more project-based learning in your classroom but have concerns
about planning projects properly, using class time wisely, and teaching standards effectively?
With these concerns in mind, Michelle Koski and I attended a PBL Design Camp at High Tech High
in San Diego, and here are some highlights of what we learned:

  1. Planning projects can be time-consuming but is doable and worth it.
  2. Yes, you can have traditional standards-based teaching with PBL, and you should!
  3. There is no “right” way to begin or plan a project.
  4. Ask students for their feedback, not just after the project but before and during the project as well.
  5. Students are PROUD of their work (not their grade).
Voice, Choice and Ownership in PBL! So, how does that happen?
At High Tech High’s PBL Design Camp, middle and high school educators from all over the country came together, each with the spark of an idea for a project. By working with their school partners and hearing critique from other camp participants, they were able to develop a project that suited the needs of their students and their teachers. 
Michelle and I are two such participants who have benefitted from the PBL design process. The idea for our cross-curricular project came while discussing two independent projects we do for our students. My Dystopian Fiction students write dystopian scenes that focus on world building, character development and action sequences. Michelle’s Costume and Fashion Design students create costumes for plays based on fashion trends. For our project, we have decided to combine the two and have Michelle’s students design costumes for my students’ writing. My writer’s will pitch their story ideas to her designers who will choose a partner to work with. The partners will meet regularly during the design phase of the costumes to work on revisions of both the writing and the costumes. 
We plan to conduct this project during fourth quarter. Here is what we hope to gain in terms of learning outcomes:
  • Both classes will learn the process of critique and revision
  • As writers, Dystopian Fiction students will learn to clearly communicate their vision with sensory imagery and vivid language.
  • As designers, Costume and Fashion Design students will learn to collaborate and communicate with a “client” in order to create a product that reflects more than the artist’s vision.

Stay tuned for the results of our project…


More Writing, Less Grading—it’s true!

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            I want
students to write more, but I want to grade less. It just so happens I found an
avenue to make this happen.
            For five
weeks in a row, I’ve had my sophomores spend the first half of block writing
about a selected passage from Jane Eyre.
During the second half of block, they use a single-point rubric to peer edit in
a round-robin fashion.
            After that,
each student decides which essay she would want to turn in for a grade. I
collect the “keepers” but I don’t grade them. The next week, after another
timed write and round of peer editing, I pass the keepers back out. Once again,
students choose between the essay they wrote today and the keeper from last
week. I collect the keepers again, and so on. It reminds me of being at the eye
doctor: “Which one is better? 1 or 2? Better here … or here?”
            Today is
the last week, and at the end of the day, I will have a stack of keepers to
grade. They will have written five in-class essays and I only have to grade
one.
            Here are some
of the benefits:
  • Students do not receive a letter
    grade until the final one, so they have to look beyond “the bottom line” and
    actually think about how they are doing
  • Students engage regularly with
    the rubric to better understand how to write well
  • Students learn to rely on their
    peers for feedback instead of seeing the teacher as the only expert in the room
  • Students rely on their instincts
    and self-evaluative skills—they take ownership of their writing
  • Each week is another opportunity
    to out-do the last keeper, so students are motivated to do their best each time
    (you should see them scribbling away!)
  • If a student misses class or has
    a bad day, she knows she will have four other opportunities, so it takes the
    stress level down
  • In-class, handwritten writing reduces
    cheating
  • It’s great for formative assessment:
    I can quickly read through the stack of keepers and intervene individually for
    comprehension gaps or writing skill gaps
  • Students are compelled to
    consider key passages from Jane Eyre
    that they may have glossed over in their reading
  • Students have choice in which of
    their essays receives a grade
  • Students practice a type of
    passage study they will see on the SAT and AP tests
  • Increased writing volume and frequency
  • Students receive instant feedback
    on the same day from their peers
  • Students get to see how 2-3 other
    students approached the same passage and prompt
  • Peer editing happens while the
    writing itself is fresh in their minds
  • Students talk to each other about
    their approaches while they do their round-robin peer editing

            I’m so
excited about how well this works and hope to adapt it going forward.  

Architect Project – Close Reading and Analysis as Tool to Imitate Writer’s

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Recently I attended the DVC English Articulation Conference with Michael Schooler and Tiz Woo. The first session I attended was very beneficial and thought-provoking and is something I will build into the Writing Seminar and AP Lit curriculum I teach next year.

Essentially, students are asked to unpack difficult quotes they encounter. Students perform a close reading and attempt to determine author’s tone and purpose. Then, students are able to begin to delve deeper into themes and messages about the human condition and society.

Finally, students begin the Architect Project in which they are asked to imitate the author’s style and voice in writing. As in all text forms (written word, music, television, film, etc.) the written and spoken work is a reflection/response to a previous text and taking a previous text/idea and expanding upon it

.

In asking students to imitate writers, the thought is they will continue to develop their style and voice as writers. I look forward to having AP Lit students work with difficult texts (ex. Heart of Darkness) as well as Writing Seminar students (ex. Glass Castle) work on imitating the voice and style of works of literature.

An Easy Way to “Flip” The Classroom Without Losing Student Discovery

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Flipped classrooms are very popular.  I see a lot of benefit in letting students have agency over their learning:  letting them learn when and where they want, and at a pace that works for them.  My main critique of the flipped classroom is that it removes most, if not all, student discovery.  Generally, videos are made that tell the students what they need to know.  Often, there’s little struggle or opportunity for students to figure things out. 

One strategy I’ve started doing is using a “flipped” approach in my classes where the “flip” is not when the learning happens but rather the roles the students and I play.  For example, today one of our class objectives was:  “I can simplify rational expressions.”  Instead of teaching the students how to do this, I put an example and the answer on the board and gave the students five minutes in their group to figure out how the answer was found.  They reverse engineered the method for simplifying rational expressions.  At the end of five minutes, the class had to teach me how to simplify.  I wrote down what they told me, synthesized their strategies and we moved on to the next skill.

This picture shows two skills done in this style.  The first is after they’ve taught me so you see the problem worked out and the strategies they came up with to do problems like these.  The second skill was the one they were working on when I took the picture.  They were working backwards to figure out how I got the answer I did. 

As I was doing this today, numerous students told me that “I like learning this way” and “This is fun” and “This is really making me think.”  I really like using this strategy when the skills can be deduced from prior knowledge.  There are of course times when they need me to introduce new concepts and there are problems that they simply cannot reverse engineer.  However, as much as we can we should require our students to discover, be resourceful and figure things out. 

I know that this works nicely in a Math class but I’d love to hear if this approach could be used in other departments and if any of us are already trying this type of “flipped” classroom.

Using Classic Coca Cola Bottles to Understand Volume of Revolution

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The final concept covered in AP Calculus AB is finding
volumes of solids. Since solid figures and

volumes are three dimensional, it is
sometimes difficult for the students to visualize a 3-dimensional figure drawn
on a 2-dimensional whiteboard. When I attended an AP Calculus Institute, I came
home with several activities and labs that I could use with my students. Some
were helpful and some were less so, but I was intrigued by the one that had
students calculate the volume of the liquid contained in a classic Coca Cola
bottle. Calculating the volume of a can is pretty simple because cans are cylindrical and their radii remain constant. The volume would be equal to the
area of the base (a circle) multiplied by the height of the can. On the other
hand, a Coca Cola bottle is curvy and while any cross section of the bottle
would be circular, the radius changes at different heights of the bottle. In
Calculus, we learn that we can find this volume by defining the area of the
cross section (a circle) as a function of the radius (written in terms of the
variable x) integrated along the height (x) of the bottle. This is not an easy
idea to convey while drawing functions on the board and trying to simulate the
function rotating around the x-axis. I hoped that having something tangible
like a bottle to demonstrate the concept would be helpful for the students so I
decided to try the activity.

I split the activity over two days. On the first day, I
handed out Coca Cola and Diet Coke bottles (they were two different sizes),
markers, tape measures and a worksheet to record data. I explained that we
would be calculating the volume and we spent a little time discussing why
calculating the volume might be difficult. The students then worked with
partners to measure the circumference of the bottles at regular heights
measured from the bottom of the bottle to the height of the liquid inside. They
entered their data into their calculators using lists and then back calculated
the varying radii using the circumference data. This allowed them to graph
their height vs. radius of their bottles and they were able to see an approximation
of the profile of one side of their bottles. They then used a quartic
regression to find an equation that best fit the data graphed. This was
completed on day one.
On the next double block period, I had planned to teach them
the lesson on calculating volumes of revolution and then afterwards ask them to
calculate the volumes of their bottles. At the last second I decided to have
them calculate the volumes before I taught the lesson. I am so glad I did this!
We were able to spend some time hypothesizing on how we could use our data to
calculate volume. Eventually we were able to draw a picture of our bottle on
the board correctly aligned with our x and y axes. They were able to see the
relationship of the varying radii of the bottle to the volume of the bottle.
When we finally determined that we were supposed to integrate, the process made
sense to them! When I then taught them the lesson (Using the disk and washer
methods to finds volumes of solids of revolution), they were able to visualize
what was happening and I didn’t have to overcome so many objections to the
process that I normally would hear from the students each year.
Actual Volumes: Diet Coke 237mL and Coke 355mL

I will admit, the lesson did not go perfectly. Everybody
overestimated the volumes significantly. We tried to adjust by estimating the
thickness of the glass, which helped, but I still think the students were not
careful enough when measuring the circumferences. In the future, I think I
would give them lengths of string to use to wrap around the bottles and then
have them measure the string with the tape measures. I think the tape measures
were too stiff for them to work with accurately.  I also think I would let the students wrestle
with the problem longer before I guided them toward integrating the area of the
cross section. However, even without these minor tweaks, I think the lesson
achieved even more than I had hoped for!

Student-Centered Good Times

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Students in my honors English 1 class are writing research papers and they will present a rendition of the TED Talk based on their papers. During the last two weeks, students were tasked with teaching their peers different skills needed in order to start these research projects. The different skills taught are 1)what makes a good TED Talk 2) public speaking skills 3) Nuts and Bolts (paraphrasing, synthesizing and MLA rules) 4) using reliable sources. These are all the skills needed in order to create a successful research paper and TED Talk. Different groups were assigned different skills that they taught/presented to the class. After each student-centered lesson, the students individually assessed the group that had just taught, and immediately “shared” the assessment with the group members. Here is a link to the peer assessment doc: https://docs.google.com/document/d/1Ka2eKoDo6QlpiThQQQzLd5e77VrBHcNmbfdp9G_gkcU/edit.

My biggest critique of skills teaching with a student-centered approach is that it takes forever. Students in each group needed to learn the information pertinent to their skills; they had to create a lesson for teaching the information; and, they had to teach their lesson to the entire class. What I could have taught in a fraction of the time, took two weeks for students to complete. Plus, two weeks ago, I had a ton of students out sick, which put off the student-centered lessons as well. The second critique that I have for this type of student learning is that students didn’t always explain the material that they were assigned to teach in a clear and coherent way, so for those situations, I have to take more time to reteach the material.

However, a couple of the groups’ lessons were awesome, and I couldn’t have done a better job myself. The public speaking groups, in both of my two honors classes, killed it! The lessons were fun, engaging and informative. They were what I assume student-centered learning is supposed to be. Students left class that day really happy, and you could tell that they fully enjoyed class.

I conducted a survey at the end of this lesson. Here is a link to the results:https://docs.google.com/forms/d/1VxlhniHoV6VNF6cgprPqR3xlsgmF41YbmaeEDZ5uNFk/edit#responses. The results are across the board. Most of the students seem ambivalent to this style of teaching/learning.

Why Are Our GIRLS So Resistant To Student-Centered Learning?

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I’ve always had a student-centered approach to teaching: my classrooms have always had tables (or desks formed into pods) and I try to limit my time standing in front of the room lecturing at the board.  My classes often involve student activities/discoveries and conversations.  The term “guide on the side” really resonates with me because I like to think of myself more as a coach than a teacher.  This may be because I actually have no formal training as a teacher.  I went to a small liberal arts college, majored in Math and Sociology and found myself figuring out how to teach as I went as a 22 year-old fresh-out-of-college young woman teaching high school students just five years younger than me.  Looking back, I realize that I was greatly influenced by my incredible department chair who had this same student-centered approach and I naturally followed her lead.  It didn’t feel new or novel and rather just became my style.

Carondelet is the fourth school I’ve taught at, the only all-girls school I’ve taught at, and the only school where I’ve received such resistance to this style of teaching.  I’m used to the usual hazing that happens to new-to-a-school teachers, but I’m surprised that I’m still dealing with fierce resistance to my style of teaching.  Given that the direction of the school is to a more student-cenered, guide-on-the-side style, I wanted to share some of the pushback I’ve received as a warning to all of us for what may be coming.

Here are some of the comments I received on a recent survey of my Algebra 2 with Trigonometry class:

[My previous math] class was very traditional and i was able to learn and do very well in that class, this class is all over the place and confusing and I’m not doing well at all.


[I prefer a traditional math classroom because] It is organized and has a plan this class room is very frustrating and all over the place I juts want to learn the section and do my homework everyday in class


I just feel really frustrated with the way we have been doing testing and learning this year.
I can’t teach myself, I need a teacher teaching me subjects or else I just don’t get it.
I DO NOT mesh well with growthmind. I like to have a sense of what will be on the test
so that I can come into class on test day feeling prepared. I feel that these growth mindset
tests do not reflect my knowledge of the information and I am just feeling very frustrated.



My whole life I have been taught math the traditional way and it is what I am used to and
it is in that format hat I understand the concepts.

I want to be in a different class with a better teacher.

I absolutely do not like the problem solving way of math. I used to love math and this way makes
me hate the subject. I need to be able to be taught a way to do something and for me to practice
what I’ve been taught so I can grow my math skills. Me teaching myself is not helping me at all and
I walk into every test scared and stressed because I don’t feel prepared even though I complete almost
every practice test and it’s really frustrating. I’m concerned that I will not be prepared
for pre-calculus next year.

This class in general makes me very anxious because I do not know what will come next and
I am a person that appreciates predictablity and control.

You may notice that some of the students above refer to a growth mindset, something I’ve been pushing hard in this group.  Also on the survey were two questions:  Where are you on the growth mindset spectrum (1 = fixed mindset, 10 = growth mindset) and what type of classroom do you prefer (1= traditional, 10 = student-centered).  These results were fascinating (p= .0013) showing that there is a significant positive relationship between students who have a growth mindset and prefer a student-centered classroom.



Here are some comments from some of our more willing students:

I like the collaborative [classroom]. It requires me to think more instead of just doing to do.


I like how we are actually making an effort to switch education


[I] much prefer the collaborative teaching style because it helps me learn from my mistakes and think through problems more. it is also more engaging.

I did realize the thoughts that go into problem solving, however actually doing a problem solving question made me feel as if I was getting somewhere. At some point I did not know how to solve it or could only solve it half way. So I think it made me think a lot more than I have in awhile which I liked.


Collaborative classrooms help me to see math in ways that I usually don’t. It doesn’t seem so black and white.


Finally, I want to pose a theory as to why our students GIRLS may be so resistant.  In reflecting on why this resistance is happening here and now, I’m thinking about the other schools that I’ve worked at.  All three were much smaller than Carondelet (class sizes closer to 12-15) and because of their smaller size perhaps more exclusive and competitive.  At those schools there was an expectation that school would be hard, challenge was expected, and although not always enjoyed, this was seldom equated with bad teaching or some form of injustice.  But, I think there is a bigger factor at play:  the fact that this is the first time I’m experiencing this in an all-girls setting.  I think in my previous schools, the boys loved the challenge, the unpredictable nature of our learning and the messiness of the class structure.  And because they loved it (or at least didn’t complain) the girls too got on board.  So, I’m finding myself challenged with motivating these girls by myself, convincing them that I am still teaching them (even if not directly) and they will be better served in college and life by having a class that isn’t neat, tidy, predictable and laid out on a platter for them.

A Number Talk Sparks Lots of Question About Student-Centered Learning

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As part of our online course, “How to Learn Math for Teachers” by Jo Boaler, he Math Department is learning about something called Number Talks.  In a number talk, more info here, students are presented with an open-ended problem and are encouraged to think of many ways to solve and many ways to represent their solution (including both numerical and visual representations).  A number talk might start with asking students how to multiply 36 x 5, for example, without a calculator and without pencil/paper (i.e. beyond the procedure traditionally taught).  These talks teach students about the flexibility of numbers, how strategy can be applied to numbers, the connections between numbers and other concepts, and the creative, artistic nature of numbers.   At the same time, it teaches them to expect multiple solutions to problems (i.e. Math is not about getting one right answers) and lets them practice explaining their ideas, methods and solutions.

I really love the idea of number talks and think that even doing a simple problem like 36 x 5 in a high school class has real benefits.  But, I’d rather find a way to change the way I’m teaching so that I use the idea of a number talk to talk about the more advanced topics that we teach in our classes.  And that’s why I was so excited when Lesley sent us a example of such a number talk that she had just played with as part of the Mindset Mathematics Leadership Conference.

It helped that I was just wrapping up a unit on radicals in Algebra 2 with Trigonometry and I was totally hooked on how to solve this visually.   I of course knew how to solve Algebraically/procedurally but this was asking for much more.  Did I really understand what a square root was?  It took me a good hour thinking hard about what a square root really is.  A finally settled on thinking of the square root as the side of one square.  But, even then it took me time to figure out what that meant, and what the expression x+15 meant.  I was thinking, not simply doing.  I was stretching my brain and it was exciting!

I finally came up with this solution and felt really satisfied with the experience:

Because we were just wrapping up this unit in Algebra 2, I decided to pose this problem to them as a number talk.  And, here’s where my failure began.  Because I was at the end of the unit, and a bit behind the other Algebra 2 class, I didn’t feel I could devote class time to actually do the number talk.  And if I’m being totally honest, I doubted that many of my students would have been able to handle it.  Instead, I put it on my board and asked students to think about it and contribute whenever they had an idea.  I told them it would live on my board for a couple of weeks and we’d see what gets filled in.  I had visions of some of my more motivated/math-interested students thinking about this as I did and using their free time to come to my room to make their contribution to my board.

Well, it’s been about two weeks and here’s what my board looks like:

Don’t be fooled.  The pictures you see have nothing to do with the problem.  That’s work by my Geometry students who needed some board space to work on their problems.  Not one student contributed to my number talk.  It’s not their fault.  To really have done this right, I needed to model it for them by using class time.  I chose not to, under pressure to stay on schedule, and perhaps missed out on a really deep Mathematical experience.

This is making me think a lot about much of the innovation we’ve been talking about both in our department and as a school.  In order to be truly student-centered, we as teachers need to be able to go off-schedule, right?  We need to have the flexibility to follow the curiosities of our students.  But, how does this work when we have a Scope & Sequence that dictates how long and which topics to cover?  Isn’t this teacher-centered?  If we are truly student-centered, are we comfortable if some sections of Algebra 2, for example, cover different topics than other sections?  How might this affect our sequential courses?  Or do we do enough re-teaching in our sequential courses that we could accommodate such a student-centered model?  Beyond sequential courses, would this compromise a student’s ability to do well on standardized tests, such as the SAT, if we go deep in one topic and miss another all together?

Sorry, that was a lot of questions but I am confused about how to do this.  Fortunately, our new Algebra 1 program will remove the timing pressure that the Scope & Sequence creates.  Students will self-pace through the material and we’re intentionally building in lots of opportunity for deep thinking activities, such as number talks.  The Scope (the curriculum), however, is still built by us, the teachers.  Might there be a way for us to make the scope more student-centered, so that students determine the concepts they cover?

I’d like to argue that if we focus on deep thinking, we can move away from our current approach of covering concepts and move toward an approach that teachers math strategy/math flexibility so that when they are presented with a topic they’ve never seen (whether on the SAT or in a later math class) they can use their mathematical intuition to figure it out.  After all, all Math concepts can be derived from basic principles.

In Praise of Nonfiction Books

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Our colleague Tiz won a prize at our Christmas party. She could pick any book in our library as her own. This week Tiz chose a book I love – Meta Maus by Art Spiegelman. I cannot explain better than the New York Times Book Review why this is such a good book , “Richly rewarding…The book also serves as a master class on the making and reading of comics”. I was so happy when Tiz choose this and pondered a bit why I was so happy. Part of the reason is I love nonfiction books. I have learned more from nonfiction books than anything else in my life. For me, and I believe for many, they are the best choice as a learning tool. And they offer me learning on my own time, schedule, interests, needs and wants.

Synthesizing information takes a lot of time, and a well-written book allows me to grasp a lot of information quickly and succinctly. I learned much about memory from MoonWalking with Einstein by Joshua Foer, without having to do all that research myself! Really, it is amazing when you think about what a well-written book pulls together for you. I learned about memory, the brain, visualization, storytelling, memorizing, and about something I didn’t even know existed,  the U.S. Memory Championship.

A good book can ignite a passion to search for more. The Shakespeare Wars by Ron Rosenbaum did that for me with Shakespeare. Before I read this book, I just could not agree with the crowning of Shakespeare as the literary king of English. “C’mon!” I would think, “it has been 400 years!” The Shakespeare Wars is about people with a passion for Shakespeare and a willingness to go into excruciating detail with and battle for his works.  By reading their debates, and experiencing their passion, I became more and more convinced of the top spot for Shakespeare.  The variations of O in the folios of Hamlet and the difference they make just astonishes me.  I had never paid any attention to the folio differences and was mesmerized by this knowledge.   This book opened up Shakespeare for me.


Books let you explore at your own pace, and in the context of your own needs.  I recently visited Boston and my daughter took me to a wonderful breakfast sandwich place, Mike and Patty’s.  This is located a block away from a Knox Street, and I asked my daughter if Knox Street was named after Henry Knox, a hero of the American Revolution, who organized a difficult transfer of cannon from upstate New York Fort Ticonderoga to Boston.  This extra artillery was key to the end of the Siege of Boston, and I would not be at all surprised if Knox was celebrated by Boston. I knew all this from having read 1776 by David McCullough and was able to pull down the appropriate chapter from my Audible account to confirm this information.  I don’t know if Boston’s Knox street is named after him, but Fort Knox is.

Michelle is working on creating a Joy of Reading in every section of the library.  Books are so important and have everything the educational buzz is all about- putting the path of learning in the reader’s hand. 

Grappling with muscle function through creativity and engineering

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One of the most difficult concepts for students to learn when it comes to muscle function is the Sliding Filament Theory of Contraction. For years I  had students make a model of the theory after giving them the details and providing most of the information at the start of the unit.  Last year, I decided I would force the students to figure the theory out while building their model.  I am honest with students from the start and explain that I am purposefully not giving them  the details and that I want them to struggle a bit to figure it out.  I promise to address misconceptions later in the process so that they can make modifications and adjustments prior to presenting.

Students start by researching the parts of the muscle required to make contraction happen.  I post a few videos on Schoology as a reference but they are invited to use any resource they choose.  The next step is to try and map out the actual steps of the theory and figure out how they will demonstrate the steps in a working model.  When ever I assign a project the fear is will the students stay on task? I haven been very pleased to hear the students talk to each other about the movement of muscles and try and explain it to each other.  I encourage them to use other students as a resource – if they hear someone explaining a part of the process they should ask them to explain and help them understand.  This process helps both sets of students the “teacher” of the material and the “student”.

Last week, the students started the project with a lot of enthusiasm, determined to figure this difficult process out.  On the rubric I provided, I reserved the last 2 points for “WOW factor”  and that brought out the competitive nature for many of these groups who are determined to “wow me” (their words).

This project is creative and allows students to use their artistic talents.  There is also an engineering component because the model has to move and the various pieces have to work together.  In the end each student will present their model to me, walking me through the specific steps of the theory of contraction and explaining their model.  I have them present individually even though they build the model as a pair.  I started this process last year to ensure that BOTH students understand the steps and can both be successful with the material.  It forces both partners to be engaged in the process and also take ownership which I believe increases the level of discussion.

I enjoy the process of letting the students “figure it out”  but I also see the need for concept checks to allow for revision and corrections.  Students in the past have reflected that this project is very challenging but they they learned a lot and won’t forget the sliding filament theory.