Grading a Project on the Learning, Not Compliance: Desmos Art Project

Two years ago I had both my Honors Algebra 2 and my Honors PreCalc classes complete a Desmos Art Project.  The students used the various functions, inequalities, and equations they learned to recreate a picture.  They had to use transformations and domain and range.  I was excited to have students do this project because they could combine math with art & tech, plus each project would be unique.  My biggest struggle was creating a rubric to grade the projects.  I looked at several online, but never found anything I really liked.  In desperation, because I needed SOMETHING, I created an absolutely horrible one that was based on the number of functions/equations they submitted; basically it was about compliance & behavior, not about learning. I knew the rubric was bad, but it was one of the moments where something is better than nothing.  Here are the directions I gave the students.  Here is the rubric. It’s awful, right?  Here’s pics in case you didn’t want to look.  You might wanna shield your eyes, it’s really bad.

I’ve long used Standards Based Grading and worked towards grades focusing on what students know, not behavior.  But that project grade was definitely more about behavior.  Ugh.  This year, when I repeated the project, I was determined to have a better rubric.  With the craziness of being a teacher and my perfectionism that results in procrastination, I almost ended up with the same one!

 

Originally, I did this project at the end of the year.  The main feedback I received from students was it was the best way for them to learn domain and range.  Based on that, this year I am doing the project early in Algebra 2.  Therefore, my Algebra 2 students have recently started the project. I found Nat Banting‘s directions that he gave his students for a Desmos Art Project and lifted some of his language to add to my directions.   You can find my updated directions here.

The biggest change is in my rubric.  I moved to what is called a single-point rubric.  The idea is basically you have a middle column that is the criteria for your students. The left side is blank for areas of improvement and the right side is blank for where the student excelled.  This was my first attempt at this type of rubric and I’m liking it so far.  I’m sure it could be better and would love feedback for how to make it better.  I have 2 more Algebra 2 courses this year that haven’t started yet, so I can actually adjust this year for future classes!

I debated a lot about the Project Management row.  It is still behavior oriented.  Yet, when we look at the skills and dispositions our students need outside of school, project management is a skill that they need.  I decided to make it a part of the grade, but a minor part.  I may regret it later.  From there, I focused on the key knowledge and understandings that I wanted students to gain from this project.  (Note: our school has heterogeneous classes where students can opt in for Honors distinction, that’s why you see one line about Honors.)  Instead of requiring a certain number of each type of function, I tried to focus on students showing their learning of each function, transformations, and domain and range.

I moved most of the behavior related part of the grade to Project Requirements.  I decided that these aren’t being graded themselves.  Either their project meets the basic requirements or it doesn’t.  If it doesn’t, I’m not grading it; I will put a zero in the grade book as a placeholder and the student needs to get the project up to meeting the basic requirements.  As I explained to my students, if my boss gives me a project, it’s not acceptable for me to do it half way.  I either meet the basics of the project or I don’t.  If I don’t, that can impact my employment. Once the student has the requirements met, I will grade their project.  The consequence for not completing an assignment, or for it being incomplete, is to complete the assignment so the student can learn.

Lastly, I require my students to self-assess on all work like this.  I had a grad school prof require this, which annoyed me at first.  However, I saw how helpful it was to my learning.  Students will submit the link to their Desmos project on a copy of the rubric where they have self-assessed.  They are to “think like a lawyer” and prove their case as to why they should be assessed on the rubric the way they are describing.  One of our art teachers will be helping the students with printing and mounting their art work.  It will be displayed for an Exhibition Night at our school!

If you have other ideas for a project like this or how to make my rubric better, please let me know! Have you used a single-point rubric before?

Day 1 – I love having students back!

Why are we all so tired at the end of day 1? Is it the adrenaline rush? I’m wiped but it was a fabulous day. I love having the energy of students back in the building. 

For my Algebra 2 classes, I used Sara Vanderwerf’s 100 game task for teaching great team work. It went FABULOUSLY! 

Here are some pics of the #firstday

Deeper Learning – Chapter 2 – Dispositions: Critical Pathways for Deeper Learning

This is the 4th in a series of posts I’m writing on the reading part of summer+ learning for my job.

Previous Posts:

Deeper Learning: The Foreword – post 1

Deeper Learning: The Introduction – post 2

Deeper Learning: Chapter 1 – Deeper Learning for Students Requires Deeper Learning for Educators <— My fave chapter for sure – post 3

On to the notes from this chapter – Dispositions: Critical Pathways for Deeper Learning

• If we are to prepare students for a vastly different future, the first task is to identify what we believe to be the critical dispositions of deeper learners and then suggest ways to design instructional and assessment strategies intended to cultivate the growth of deeper learners over time.
• Deeper learning …will necessitate transforming the educational process from a content-oriented, subject-centered, test-driven frame to a view of education being dispositional in nature.
  • Response: This makes me a bit nervous.  Definitely need to read more to understand what they mean.
• There are a variety of views on what those dispositions should be.  In general, problem solving, collaboration, critical thinking, and effective communication.
  • Response: These are also 4 of the MV Mindsets.  The other 2 are creative thinking & ethical decision making.  Creative thinking was in one of the lists in the book.  What concerns me is only one of the models in the book mentioned ethics.  The others mean nothing if the person employing them is unethical.  I can see how this chapter would be a good all-school read since we will be assessing mindsets in all grades this year.
  • I’m still not convinced that dispositions should be the focus of education.  I see it as the undergirding for the learning of content.
• Dispositions are under our control – we can consciously, intentionally choose to employ them rather than being mindlessly on autopilot
• Sixteen dispositions of deeper learners – what intelligent people do when confronted with problems. these dispositions are journeys of continuous learning
  • 1. persisting
  • 2. managing impulsivity
    • Response: This makes me think of maturity.  As we mature, we understand more of cause & effect and thinking before speaking.  
  • 3. listening with understanding and empathy
    • Response: empathy is a major part of design thinking, which our school has embraced. creating solutions to problems that have an end user – empathize with the end user.
  • 4. thinking flexibly – open-minded, ability to change your thinking based on new information,
  • 5. thinking about your thinking (metacognition)
  • 6. striving for accuracy and precision
  • 7. questioning and problem posing
  • 8. applying past knowledge to novel situations
  • 9. thinking and communicating with clarity and precision
    • Response: reading the description makes me think they are talking about avoiding exaggeration
  • 10. gathering data through all senses
  • 11. creating, imagining, and innovating
  • 12. responding with wonderment and awe
  • 13. taking responsible risks
  • 14. finding humor
  • 15. thinking interdependently
  • 16. remaining open to continuous learning
  • Response: I’m not sold that deeper learners have to have all of these dispositions.  I know the authors said that there are journeys for each of the dispositions, but I get the impression that all 16 are supposed to be there in some way shape or form.
  • Authors believe when confronted with problematic situations, these dispositions serve as an internal compass. It might be referred to as inner self-coaching.  They argue these dispositions are more important than content knowledge.
    • Response: Why does it have to be one or the other?  I have difficulty when people say that content knowledge isn’t as important.  This is said by people who have content knowledge.  They don’t know what it would be like to go through life without the content knowledge they already have.  Plus when we think about scaffolding and building on prior knowledge, one must have content knowledge to actually build on.
• Cultivating deeper learning with dispositions in mind
  • suggest dispositions become goals of curriculum & teachers deliberately teach & assess them.
    • Response: Again, I’m not against these dispositions & I do agree they should be taught and assessed. I’m glad we will assessing the mindsets specifically.  I just don’t think they are primary goals, but secondary goals.
  • 7 strategies to help students own the dispositions
    • 1. making dispositions explicit by establishing expectations
      • make sure to offer positive, descriptive feedback (not praise) to students when we are coaching them
    • 2. develop a common and consistent vocabulary throughout the culture of the classroom, the school, and the community
      • Response: When I first came to my current school, this is something that stood out to me.  Our school has done an excellent job of this.
    • 3. transferring and applying the disposition in many settings, circumstances, contexts, and situations
    • 4. operational dispositions as action
    • 5. building the vocabulary of deeper learning
      • Why did you do that? becomes “what was going on inside your head when you did that?”
      • why do you say that? becomes “from whose perspective are you seeing that?”
      • was that a good choice? becomes “what criteria did you have in mind as you made that choice?”
      • what are you going to do next time? becomes “what will you be aware of next time?”
    • 6. reflecting on the use of dispositions and setting goals for improvement
    • 7. modeling

 

Deeper Learning: Chapter 1 – Deeper Learning for Students Requires Deeper Learning for Educators

I was so eager to read this chapter of our summer+ learning faculty reading from Deeper Learning: Beyond 21st Century Skills.  Something that I heard Dylan Wiliam say back at NCTM in April 2017 has stuck with me – “Teachers need a habit change more than they need more knowledge.” How do we move teachers from knowledge to action? I wish this chapter had been required reading for all of our Upper School teachers and not an optional one.  Excellent read and glad I chose this chapter.

Deeper Learning: The Foreword (part 1 of my notes)

Deeper Learning: The Introduction (part 2 of my notes)

Notes on Deeper Learning: Beyond 21st Century Skills – Chapter 1: Deeper Learning for Students Requires Deeper Learning for Educators by Richard DuFour & Rebecca DuFour

• Where our education currently stands
  • Our education has gotten better than in the past, contrary to reports.
  • The percentage of high school graduates keeps increasing
  • More student are taking honors & AP classes.
  • However, a good high school education is only preparing our students to live in the 1960’s!
  • Yet, 37% of our student who enter college require remedial courses (p. 28)
• Economic shifts
  • In 1970, 74% of the middle class was made up of HS graduates and dropouts.  By 2007, only 31% of the middle class was from these groups.
  • In the same time period, the middle class with postsecondary education went from 26% to 61%.
  • Between 2010-2020, only 7% of jobs will be available for HS graduate and dropouts; those are limited to either low paying or declining in numbers.
  • Postsecondary education & training is no longer just the preferred pathway to the middle class, it is increasingly the only pathway.
• What this data means
  • All HS students need the deeper learning that used to only be required for our best & brightest. (p.23)
    • Response: A bit of a push back here.  Why have we allowed good job training in HS to basically go away? Where students could learn how to be a mechanic before they graduated and had a job lined up? I just don’t believe everyone needs to go to college or should go to college.  They do need either job training or college though.  I’d like to see that job training go back to being part of high school.
  • The most promising strategy is to develop the capacity of educators to function as members of collaborative teams within a high-performing professional learning community (PLC). (p.23)
    • Response: What makes a PLC “high-performing”? What kind of leadership is needed to make this happen?
• What is a PLC?
  • “an ongoing process in which educators work collaboratively in recurring cycles of collective inquiry and action research to achieve better results for the students they serve” (DuFour, DuFour, Eaker, & Many, 2010, p.11).
    • Response: What if some the educators in the PLC are resistant to change? 
  • 3 big ideas drive PLC process
    • 1. All students learn at high levels. 4 critical questions
      • a. What is it we expect all students to know and be able to do as a result of each essential standard we teach?
      • b. How will we know when each student has learned?
        • Response: This is SO key! Formative assessment is to inform us, the educators, about next steps.  It doesn’t happen enough.
      • c. How will we respond when, at the end of a unit, some students have not learned?
        • Response: Great question.  I find this difficult in math because of the time pressure to keep moving on.  How can I circle back with those students who are struggling?  Or, will our newer method of lagging assessment help in this area so that all students have the time needed to master concepts?
      • d. How will we enrich and extend the learning for students who have demonstrated proficiency:
        • Response:  Another difficult one for me.  In the past, I had students complain that they had more work. Obviously I didn’t pick the right extensions or way to offer those extensions to the students.  I need to work on this.
    • 2. Collaborative teams of educators need to work interdependently to achieve shared goals for which members are mutually accountable.
      • Response: What if the goals aren’t shared? I’m assuming the goals are that of the particular school or school system. This can be tricky in the hiring process.  Some people are good in interviews but not so great as employees.  Other times you are desperate for a teacher in a high need discipline and don’t have a lot of options.  
    • 3. Educators use evidence of student learning to inform and improve their professional practice & to better meet the needs of individual students.
• What is Deeper Learning (pg. 24-25)
  • “the process through which an individual becomes capable of taking what was learned in one situation and applying it to new situations (i.e. transfer)…by developing cognitive, interpersonal, and intrapersonal competencies.”
  • Recommend Webb’s modification of Bloom’s and using the 4 DOK levels
    • DOK 1 – Recall of a fact, term, concept, or procedure – basic comprehension
    • DOK 2 – Application of concepts or procedures involving some mental processing
    • DOK 3 – Applications requiring abstract thinking, reasoning, or more complex inferences
    • DOK 4 – Extended analysis or investigation that requires synthesis and analysis across multiple contexts and non-routine applications.
• Projected increase in rigor on state standardized tests under the CCSS
  • All students will be assessed with items at DOK 3 & 4
  • 70% of items in mathematics will be assessed at DOK 3 or 4 levels
    • Response: This is HUGE! Lots of students pass math classes but struggle with these higher levels of DOK.  I go back and forth on this.  In one sense, I believe all students can learn math at higher levels & I want them to.  However, I also think students who pass with a basic understanding still passed and not sure that means they should be considered deficient on a standardized test.  As a private school teacher, I didn’t know this because our students don’t take these tests.
  • All students will be assessed at DOK 3 & 4 in language arts
  • 68% of items in reading will be assessed at DOK 3 & 4
• Addressing Common Core through PLCs
  • They are organized by grade level or content.
    • Response: I love my school.  I wish we had content leads and more work in HS organized around content. I do interdisciplinary work as well & will continue to do so, but I have to know the math content and how to be a good math instructor.  I hope our school will organize PLCs around content in the HS (or around groups like STEM/STEAM & Humanities).
  • The deeper learning of the CCSS certainly lends itself to interdisciplinary efforts that cut across subject areas, but we recommend that these efforts come later in the process.  In the initial stages of teaching and assessing for deeper learning, job-alike teams represent the best structure for collective inquiry.
    • Response: YES! This is what I just said above.  I think in our quest to go interdisciplinary, we didn’t make sure that teachers were solid in their own content and pedagogy first.  Too many things at once overwhelm people.
  • Collective inquiry starts with why before the how.
• Moral purpose is not enough
  • “the quality of an education system cannot exceed the quality of its teachers. The only way to improve outcomes is to improve teaching.”
  • If Ss are to learn at deeper levels, schools must create the conditions that allow for the ongoing, deeper learning of the educators who serve those students in each of the three critical areas  (1) curriculum, (2) pedagogy, and (3) authentic assessment.
    • Response: YES to both of these!!  Something I struggle with – it seems as if people think everyone in the room has an opinion of equal weight.  I don’t get this.  If I were a novice to something, say programming on a computer, and I were in a room of experienced programmers, I don’t think my voice/opinion should carry the same weight.  In teaching, I haven’t seen it work that way.  I’ve watched our teams make poor educational decisions because the “majority” were people who don’t have the same understanding of curriculum, pedagogy, and assessment as more experienced & more educated teachers.  This is nonsense to me. 
    • Edited to add:  I think the top thing our school needs to do to help in these 3 critical areas is to address the faculty turnover rate.  Our turnover rate is high and we don’t do exit interviews.  I understand exit interviews are like summative assessments, they are post-mortems, but I think they still need to be done.  More importantly, some type of “formative assessments” should be done by admin/leadership to determine where teachers are throughout the year.  This has to be done in a way where the faculty don’t fear for their jobs by being honest.  IMO, this is the #1 priority our school needs to work on.  The work we do yearly on hiring & then training new faculty is exhausting, time consuming, and drains resources.
  • Curriculum
    • Challenge – how to best ensure that each teacher is clear about and committed to teaching the essential standards.
    • It is not unusual to see a huge gap between the intended curriculum and the implemented curriculum
    • With this gap it is common to see 2 things:
      • students receiving vastly different curriculum based on their teacher
      • admin being very “top-down” and regulating every single thing.  this fails to generate the clarity, coherence, or commitment to the curriculum. No involvement = no commitment
    • The only way to guarantee a curriculum is if the teachers who will deliver the curriculum have worked collaboratively to:
      • study the intended curriculum
      • agree on priorities within the curriculum
        • Response: what if there isn’t agreement?
      • clarify how the curriculum translates into student knowledge & skills
      • establish general pacing guidelines for delivering curriculum
      • commit to one another that they will, in fact, teach the agreed-upon curriculum
        • Response: Again, what if teachers make this commitment to the team and then still do it different in their classroom because they didn’t agree on the priorities?
        • When done well, a team will regard the essential skills of a guaranteed curriculum…as a promise they are making to students and to one another about what each student will learn.
  • Pedagogy
    • “a bad curriculum well taught is invariable a better experience for students than a good curriculum badly taught: pedagogy trumps curriculum” ~ Dylan Wiliam
    • well designed, inquiry based problems & tasks
    • build on prior knowledge – scaffold
    • clearly defined standards of proficiency
    • students receive formative feedback as the move forward towards those clearly defined standards
    • students engage in frequent, small-group collaboration
    • teachers help students develop their meta cognitive skills
    • teachers of deeper learning expect students to access, evaluate, and explain competing information about issues; develop & respond to probing questions; work collaboratively; justify their answers
    • Inquiry based does not mean unstructured or minimal guidance (emphasis mine)
    • Inquiry based is still designed in a structured way to lead students to the learning goal – balance students’ need for direct instruction with opportunities to inquire
    • students must explicitly be taught norms that foster healthy, collaborative group work to function as a team
      • accountability for the team as well as individuals
    • no one can script instruction that is guaranteed to result in deeper learning
    • the ultimate test of effective instruction (using solid pedagogy) is actual evidence that students have learned
  • Authentic Assessment (while I love all 3 – curriculum, pedagogy/instruction, and assessment; assessment has always been my biggest interest)
    • widespread agreement that assessments must change if they are to promote & measure deeper learning
    • high quality assessment could serve as a catalyst for improved instruction because if “assessments measure deeper learning abilities, teachers are more likely to teach the relevant skills.”
    • collaborative teams must help each other develop excellent formative assessment skills
    • Dylan Wiliam’s Embedded Formative Assessment is an excellent resource for PLC teams
    • teachers can learn what they need to know about writing good assessments by reading an article or introductory text on the topic
      • Response: Pet peeve of mine, which relates to something I mentioned under pedagogy, why don’t schools of education focus more on teaching about how to do assessment?! In my 2 year MA in Education program – not one class on assessment.  In my 2 year Ed.S program – 1 class on assessment. It’s a topic I love, so I’ve read a lot of research, etc.  However, most teachers have had little to know learning on this topic.  They just assess the same way they were assessed.
    • They recommend looking at PARCC and Smarter Balanced tests to get an idea of how students will be formally assessed.  Since I’m at a private school our students don’t do this.  I do think it is important to take a look at SAT & ACT exams since most students still need to take one of them for college admission.
    • the effort to have high quality, authentic assessment will have no result on student learning unless educators use the results to respond to the needs of the individual students & to inform the educator’s professional practice
    • team created common assessments are a means to an end – they assess the agreed upon meaning of the standard/learning outcome
      • Response: what if only 1 teacher instructs a certain course? how to get the team together to write these common assessments? what if not all team members see this as necessary?
      • these common assessments are an instrument for identifying students who are unable to demonstrate proficiency – this helps students and teachers
• When students don’t learn – in a PLC school, collaborative teams of educators analyze the evidence of student learning from frequent common formative assessments to ensure that students who are struggling receive additional time and support for learning that extends beyond the individual classroom teacher to a include a schoolwide plan of intervention.  This intervention must be:
  • timely
  • diagnostic
  • directive
  • fluid and flexible
  • systematic
    • Response: Amen & amen to this whole bit about supporting students. This reminds me of the recommendations in NCTM Principles to Action for additional support for students who need additional time/help.  It is the school’s responsibility to help students in these areas.  If we accept a student in our private school, we are saying they can be successful.  
• Common Formative Assessment as a catalyst for professional learning
  • in a PLC, use the evidence of student learning as a feedback loop to analyze the impact of their professional practice
    • Response: In our school – how do we get this to happen? 
    • if the assessment reveals one colleague has exceptional results with a skill or concept, that person can share strategies with colleagues
    • if the assessment reveals one colleague has had difficulty to help their students reach proficiency with a skill, the team can brainstorm ways that the teacher can integrate new instructional strategies
  • **Using evidence of student learning to inform and improve professional practice is the sine qua non of a PLC.**
  • Hattie concludes that schools should have systems in place to ensure that:
    • educators are working as members of a team & not in isolation
    • there is a shared understanding of the knowledge, skills, and dispositions all students must acquire
    • evidence of student learning is collected in a regular & dependable way
    • students are provided with multiple opportunities to demonstrate their learning
    • educators use the evidence of student learning to examine their teaching
• Key to helping students is to invest in ongoing professional development
  • educators must assess the quality of their instruction on the basis of actual evidence from team created common assessments
  • when a team discovers none of its members are being effective in helping students with a concept, then they must seek assistance from others
    • they must be supported in this ongoing learning at the same time they are held accountable for sustaining their collective inquiry until there is tangible evidence of improved results
  • How do teachers develop the assessment literacy that can serve as a catalyst for improved pedagogical practice?  Again, work as collaborative teams to build common assessments instead of working as individuals.
    • Collaborative teaming is considered essential to building the assessment literacy of educators (emphasis mine)
  • best way to deliver solid PD to teachers – ensure that the school is operating as a professional learning community (PLC)
  • Therefore, school leaders must:
    • establish moral imperative of helping all students (emphasis mine)
    • assigning teachers into meaningful teams that share a collective responsibility for helping students (emphasis mine)
    • providing time for teachers to work together on curriculum, instruction, and assessment as part of their routine practice

Deeper Learning: The Introduction

Our faculty is reading 4 chapters of Deeper Learning: Beyond 21st Century Skills for part of our summer+ learning.  This is part 2 of my notes.

Deeper Learning: The Foreword – part 1

Deeper Learning: The Introduction – part 2 (this post)

Deeper Learning: Chapter 1 – Deeper Learning for Students Requires Deeper Learning for Educators <— My fave chapter for sure – part 3

The Introduction

• “Researchers are not only identifying new ways of learning; they are also pinpointing the best practices in instruction, curriculum, assessment, and leadership that show the highest promise for transforming learning from the superficial recall and regurgitation of facts, figures, and procedures to the intentional development of crucial cognitive skills (News from the National Academies, 2012)” (p. 3).
  • My response: When will admin & teacher actions match what we know from research? I tend to think too many teachers have more autonomy than they are actually ready for as they are still novices.
• Hewlett Foundation has 6 attributes of deeper learning (p. 3-6)
  • Mastery of core academic content
  • Critical thinking  & problem solving
  • Collaboration – research on collaboration shows it is one of the most powerful tools to raise student achievement (Hattie; Marzano)
  • Communication in writing and speaking
  • Self-directed learning
  • Academic mindset
    • My response: Several of these are also MV Mindsets.  I believe our school is on the right track.
• Teachers with a deeper learning agenda do more than ask students to memorize facts and procedures, practice skills for rote recall over and over on worksheets, and fill in the blanks on quizzes and tests (p.7).
• Deeper learning is a process that enables students to become more proficient at developing the fullest possible insights into the meaning of curricular content relevant to college and careers in this century (p. 8).
• Deeper learning is an outcome that results from the self-directed transfer of the 4Cs to the student’s understanding of a concept’s meaning (p.9).
• My response: I notice that my main areas of interest are really around changing teacher beliefs & actions to best help students.

 

Deeper Learning: The Foreword

I wrote this blog post over a month ago and forgot to hit “publish.”  Oops!

Raise your hand if you are reading a great book/paper/article and then you end up on a rabbit trail to look up the sources in said book/paper/article.  I hope I’m not alone with my hand up!

Faculty at our school are reading parts of Deeper Learning: Beyond 21st Century Skills, James A. Bellanca, ed.  We’ve been tasked to read the Introduction, Chapter 2, and then 2 more chapters of our choice.  Well I can’t even make it past “The Foreword” without a blog post! Yes, I know, that means I haven’t even gotten to the required reading yet.  The foreword kept referencing the same report over and over, so I had to look it up; all 242 pages.  Since I didn’t have time to read all 242 pages if I’m to do my other summer work, I mostly skimmed.  But it looks like excellent reading.

BTW, if you can relate to this meme, you are one of my peeps.

As I read the foreword, I couldn’t help thinking of the awesome CPM curriculum (@CPMmath) that we piloted last year and are adopting for next year.  I also was struck that these ideas about Deeper Learning are what we’ve been doing in math education for years.  Is this not as prevalent in other disciplines? Is he (James Pellegrino) just getting everyone up to speed on the basics of Deeper Learning?  Is this a book designed for the novice, experienced, or advanced teacher who understands teaching for transfer?

In bullet point form, here are the points that resonated with me.

• deeper learning can most simply be defined as learning for transfer (p. xvi)
• through deeper learning, individuals understand when, how, and why to apply what they’ve learned (p. xvi)
• 3 broad domains: cognitive, intrapersonal, interpersonal (p. xvi)
  • Cognitive competencies show consistent, positive correlations of modest size w/ students’ achieving higher levels of education, higher earnings, and better health. (p. xvii)
    • My response: Wanna help to lift up those who aren’t as privileged? Wanna decrease incarceration rates? Wanna decrease those on public assistance? Make sure that every. single. student. gets an excellent education. None of this garbage where money for schools is based on property taxes.  That perpetuates the cycle that students in poorer areas have less funding for their education.  Those are typically the students who need more funding for smaller schools and smaller class sizes, in addition to certain social services.
  • Intrapersonal competencies, conscientiousness – which includes such characteristics as being organized, responsible, and hardworking – shows the strongest relationship with these same desirable outcomes (higher levels of education, higher earnings, & better health). (p.xvii)
    • My response: As educators, it is our duty to also teach responsibility and organization skills.  They make a difference in the lives of our students for years beyond the time they have with us.  Some students struggle with executive functioning and will need additional support in these areas.
  • Antisocial behavior, which reflects deficits in both intrapersonal & interpersonal competencies, is related to poorer outcomes. (p. xvii)
    • My response: This hurts my heart and I’m not sure how to work well with these types of students.  This is an area where I need help and to grow.
  • While more research is needed & we can’t say causation at this point, only notice correlation, “this much is known, mastery of academic subject matter is not possible without deeper learning.” (p. xvii)
• Deeper learning & the development of 21st century competencies do not happen separately from learning academic content (p. xix).  <— This is why we are assessing the MV Mindsets!
• Hallmarks of teaching mathematics for understanding include:
  • The use of cognitively demanding mathematical tasks drawn from a broad array of content areas
  • The use of teaching practices that support collaboration and discourse among students and that engage them in mathematical reasoning and explanation, real-world applications, and use of technology or physical models (p. xx).
• The Standards for Mathematical Practice (SMPs) give some attention to the intrapersonal competencies of self-regulation, persistence, and the development of an identity as someone who can do mathematics (p. xxi).  (Emphasis mine)
• Creating more specific instructional materials & strategies to help students develop transferable competencies requires additional research (p. xxi).
• Multiple stakeholder groups should actively support the development and use of curriculum and instructional programs that include research-based teaching methods to foster deeper learning (p. xxi).
• Assessment must change to capture deeper learning (p. xxii).
• Current approaches to teacher development need to change substantially to support deeper learning and the development of transferable knowledge & skills (p. xxii).  Do this by strengthening:
  • teachers’ understanding of their subject matter
  • their knowledge of how student learn
  • and their awareness of students’ common misconceptions about the subject matter
    • My thoughts: I find that too many teachers aren’t interested in increasing their knowledge of how students learn OR they aren’t interested in changing their methods if if they do know these things
  • Such environments are best structured as professional learning communities and require strong administrative support.

All posts in this series:

Deeper Learning: The Foreword – post 1 (this post)

Deeper Learning: The Introduction – post 2

Deeper Learning: Chapter 1 – Deeper Learning for Students Requires Deeper Learning for Educators <— My fave chapter for sure. – post 3

NCTM 2017 Presentation: Using Design Thinking to Drive STEM PBL

Thank you for attending our presentation!

Looking for the DEEP DT Playbook?  Go here.

Our Slides

Excel Spreadsheet that can help with Project Design.

Here is a 5 minute video with some reflections from students at the end of the Bike Project in 2016.

Earning Badges

Our Head of Middle School, Chip Houston, issued a blogging challenge to the whole school faculty.  We were to blog 10 times in 12 days.  I’ve made it and earned a blogger badge! I didn’t think I’d really care about the badge, but I realized I do care.  It’s like the badges on my Fitbit.  At first I thought they were silly.  Then, I wanted more and more badges.  One time, after a big hike at Lake Tahoe and getting 125 flights of stairs, I was determined to get the next badge for stairs.  I hiked up out of the parking lot to the road so I’d get more flights of stairs.  My hubby drove the car alongside me in case I decided I was done.  The park ranger stopped to make sure I was ok and that my hubby wasn’t a creeper! ha! Then, when we got back to the hotel, I had surpassed the 150 flights and was so close to the next one, that I walked the stairs up to my room.  All to get to the next badge level.

I’m now wondering how badging impacts students.  Do they care? Do they want badges like I want badges? Do you have to be a competitive person to want a badge? Because, I’m a pretty competitive person.

Thanks, Chip, for inspiring me & challenging me to blog!  I’ve learned a lot about myself and now have archived some important learning for my teaching.

Alg2 – Investment Project part 3 – My Reflections

I’ve been blogging about an Investment Project I did in my Algebra 2 classes this past semester.  Part 1 gave an overview of the project and shared my docs.  Part 2 gave examples of student work and their feedback.  This last blog in the series shares my reflections.

Timing:

• I definitely gave the students too many deliverables in too short of a time period.  The research took longer than I predicted.
• I also had the students complete some textbook work during the project.  I was so worried about timing of my class and “coverage.”  I would not do this in the future.  We would only focus on the project and nothing else.
• I like the deliverables and don’t think I’d change any, even though some students disliked the final paper.  I saw too many benefits from what I read in the work.
• I would extend the project by 2 days if I kept everything else the same.
• In class, I would make sure students wrapped up their work with 5-10 minutes left so they could journal before leaving for the day.
• I believe in depth over breadth, I need to remember that and live it in my classroom.

The Project Itself:

• I like the topic – it is something my students are interested in
• I wonder how to make the project more authentic and if that matters? Mutual funds don’t grow at the same rate for 50 years.  They are also based on a share price, which I didn’t address.  Is it ok that it’s semi-realistic and gives students a basic intro to investments and how exponential growth works?
• I like having students create what should be in the presentations.
• I wonder if I should have students co-create the rubric like I originally planned?  If I did this, I think I might need to add 3 days instead of 2 days.
• I like having students have to “prove” why they should get top scores on the rubric and have to self-assess.  I would change the rubric so that the top points are next to the topics (on the left) and the lowest points are on the right.
• I wonder if there is a way to include logarithms without teaching them logarithms?  For example, I could have them determine how long it would take to double their investment by doing guess and check.  We do that with a zombie problem I got from Julie Reulbach.
• I mentioned in Part 2 that my students were stressed because I was gone from class one day.  I actually think this worked out perfectly.  Good PBL is more about students researching and discovering instead of me being the person with all of the answers.  This forced them to not rely on me as much.  Yes, many of them were annoyed that day; I’m ok with that.  In their final papers & presentations, overwhelmingly they talked about how the project was difficult and challenging at times, but they worked through it and learned so much.  They learned how to persevere as learners.  To me, that made it all worth it.
• I wonder how I can grade these faster? I spent way too much time grading – it took forever and wasn’t fair to my students.  I think I need tips from my ELA and Social Studies colleagues.
• I really had a hard time giving up so much class time to a topic I would normally spend one day on.  However, reading the student papers changed my mind completely.  I was teary eyed reading their papers, so proud of their work.  It affirmed to me how important this type of learning is for my students.  I don’t think math classes can completely be taught with project based learning, nor should they, but it should be a part of the course.

Alg2 – Investment Project part 2 – student work & feedback

Yesterday, I blogged the particulars of this project, including the documents I used with students.  If you haven’t looked at that yet, I suggest giving it a quick once over to get some background for this post.  Today I share some student work &  their feedback.  I’ve decided to leave my reflections for part 3 as this blog post got really long!  In the words of Samuel L. Jackson in the original Jurassic Park, “hold on to your butts!”

Student Work:

I wish I had exemplars when the project started to share with the students.  Alas, since it was my first time doing this project, I had nothing; so, I gave fairly detailed instructions (like a checklist), yet also tried to leave room for student ideas and inspiration.  Students completed a notes page of their initial findings, 3 journal writes, predictions of a 1-time investment, predictions when contributions continue, a presentation, and a 3 page-ish summary/review.  For the final paper, each cohort group brainstormed what should be in the presentation and I added it to our class webpages.  They were assessed on whether or not they included the things that we decided as a class should be there.  As a reminder, here is the rubric.  After the project was completed, I shared exemplar work with the students so they could see top level work. This was powerful. I’m so excited I have this in place for next year!

Journal Day 1: Students were to reflect on their investing and the MV Mindset of Ethical Decision Maker.  This is the final paragraph of a student who earned a top grade on the journal.  You can read her entire journal here.

Journal Day 2:  One student did a video journal instead of a written journal.  It was incredible! I loved that students knew they could step outside of the box.  She probably reflected more in that video journal than anyone did in writing.

Investment Prediction Contributions Continue: Students had to do predictions of one time investments and if they added a total of $1,000/year.  They could determine how to split the $1,000/yr between their 3 funds. These predictions when contributions continue are much more complicated and most students used recursion on their calculator.  This is one of the top pieces of student work.  Here is  snippet of what the student submitted.

 

Presentation:  There were many students that rocked the presentation part of the project, both with their content and their presentation skills.  Students were excellent at engaging the audience and using humor.  This presentation stood out for many reasons (you can see the whole presentation here.)

First, look at this slide where the girls put their comparisons on one slide, color coded it, and had the formula in the top right corner.  This was an excellent use of a graph that immediately gave a visual of their results.

The next two slides were hysterical and, again, you knew exactly what was being communicated by the use of graphs.

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Investment Paper:  This was many students least favorite part of the project.  Many thought it was not necessary.  A few actually enjoyed this part and saw their work coming together.  I do think it was important because of the necessity to summarize their learning.  The paper that was the biggest standout used a lot of graphs and charts well, not just for the sake of adding a graph/chart to take up room.  The student didn’t use MLA and I decided I didn’t care because he went so above and beyond in the layout and content of the paper.  It looked professional.  The entire paper is here.   I’m sharing his introduction, a chart, and his final reflection and feedback for me.  One student did her final paper as an infographic (same student who did the video journal), again, it was amazeballs!

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Student Self-Assessment: I had the students self-assess as the final piece of the project.  They filled out the rubric on themselves and had to defend why they should get the top grade in each category.  If they didn’t submit the rubric, they couldn’t get the highest marks. In general, students did a thorough job of self-assessment.  In 2 of my classes, all students ended up with a grade within 5 points of their self-assessment.  In 1 class, most were close, but there were a few that were way off.  For example, I had one student who didn’t answer any of the journal prompts, just described his work on the project.  He gave himself top marks on the journals and I assessed him at 0 on the journals.  He felt he should get something for the effort because he turned something in.  I disagreed and let him know that his answers to the prompts were similar to me asking a quadratic question on a test about projectile motion and his solution having nothing to do with that particular question.  That helped him seem to get it, but I still think he thought I was being petty.

I’m sharing some assessments where students thought they should get the highest grade and where they acknowledged it wasn’t their best work.

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Student Feedback and Reflections:

All but one student said this was a worthwhile project that should be repeated.  One of the most common comments was that they enjoyed doing math that was “real-world” based.  I pretty much hate that phrase, but that’s ok, I get their point, it was math they saw useful no matter what they were going to do in college and career.  They thought there were too many deliverables in too little time, they would have liked more time to complete the project or less deliverables if the time frame stayed the same.

I was absent one day due to an observation at another school.  Initially, I was stressed out about this, but then was grateful, which I’ll share more about in the next post.  The students were stressed and hated that I was gone one day.

Some individual comments:

• There was too much writing for a math class
• I liked how we combined math, literature, social studies, and economics
• Originally, when we started this project, my main motive for trying so hard was for a good grade.  However, when I really started opening up my mind to this, I began to see I wanted to learn more about the world of finance and investments.  Therefore, the further along I got in this project, I found myself not thinking about the grade as much as I thought about my desire to learn more.  (Side note: Yeah, I got teary reading several of these! Teacher win!)
• I believe that reflections are what help us grow because we can be learning great things, but if we don’t take time to reflect, it practically goes in one ear and out the other.  (This came from an iDiploma student.  I found the iD students were excellent at reflection.)
• I would say the most enjoyable part of this project was finding out what to do with my money when given this freedom.  I enjoyed having (fake) responsibility to see what it was like to handle large amounts of money.
• This project has completely changed my view on how to grow my money by teaching me about a new way to invest.
• This project has taught me so much about how to invest my money, the most important of which probably being not to wait and start investing now because you can’t make up time, and in Mrs. Mathews’ words, “YOU WILL DIE!”
• The most important thing I learned through all of this is to invest early and spend smart.
• I feel like the majority of this was done at home and I wish I could have collaborated more with my partner face to face.
• Reflection – while this wasn’t my favorite part of the project, I slowly began to understand the importance of reflecting.  At the end of the day it was nice to have that time to contemplate my daily work.  Reflecting really “cemented” the learning.
• It is challenging for me to accept that some things are going to be confusing and that is ok to leave some things unknown.
• While I did hear you when you emphasized on the importance of investing early, it was very different to actually see the large amount of money we would gain over fifty years.
• My dad helped me with some of my confusion.  He showed me his portfolios and what he’s been investing in since before I was born. I’m so glad I asked him because if I didn’t and if he didn’t physically show me what it all means, I probably wouldn’t have understood the project as much as I did.

If you have made it this far, thank YOU! I’m so proud of my students and they gave me a lot of food for thought for next time!

Part 1 – the docs

Part 3 – my reflections