Another article from the International Academy of Education’s Educational Practices Series.
- Focus on valued student outcomes
- Worthwhile content
- Integration of content and skills
- Assessment for professional inquiry
- Multiple opportunities to learn and apply information
- Approaches responsive to learning processes
- Opportunities to process new learning with others
- Knowledgeable expertise
- Active Leadership
- Maintaining Momentum
My thoughts/favourite quotes/summaries
- “Success needs to be defined not in terms of teacher mastery of new strategies, but in terms of the impact that changed practice has on valued outcomes.”
- “While some well-grounded principles [about teaching effectively] have been established, unproven ideas continue to sweep through different educational jurisdictions.”
- “Theory and practice need to be integrated”. Teachers need to be able to practice new approaches, but by understanding the theory underlying these new approaches, teachers will be more effective, as they can tailor these new practices.
- “Teachers need sophisticated assessment skills if they are to identify (i) what their students know and can do in relation to valued outcomes and (ii) what further learning they themselves need if they are to assist their students in learning. Assessment of this kind cannot take place outside of the teaching–learning process—it is integral to it. Teachers, therefore, need a variety of ways of assessing their
students’ progress, ways that include, but go beyond, standardised testing. These include interviews with students about their learning, systematic analysis of student work, and classroom observations…This use of assessment information is very different from traditional uses, such as sorting and labelling students or making summative judgements about teaching quality. “
- “For substantive learning, such as that involved in improving their students’ reading comprehension, mathematical problem solving, or scientific reasoning, teachers need extended time in which to learn and change. In such cases, it typically takes one to two years for teachers to understand how existing beliefs and practices are different from those being promoted, to build the required pedagogical content knowledge, and to change practice. Given that teachers engaged in professional learning are simultaneously maintaining a teaching
workload, and that many of their existing assumptions about effective practice are being challenged, it is not surprising that so much time is required…In any learning situation, learners may be present physically but lack commitment to the learning process. In the case of teachers’ professional learning, participation is sometimes made voluntary as a way to minimise this problem. The research evidence, however, does not support this approach.”
- ” In the case of mathematics and science, for example, existing curricula usually emphasise computational and factual knowledge while new curricula typically emphasise reasoning and problem-solving skills. This kind of change involves more than learning new knowledge and skills. It requires that teachers understand both the limitations of the current emphasis and the new ways of deciding what knowledge is valued.”
- Teacher learner communities can work, but they can also not work… What the communites have in common that work are that they are “focused on becoming responsive to students”.
- “Experts need to know the content of the relevant curricula and what teaching practices make a difference for students. They need to be able to make new knowledge and skills meaningful to teachers and manageable within their practice contexts, to connect theory and practice in ways that teachers find helpful, and to develop teachers’ ability to use inquiry and assessment data to inform their teaching. Not everyone engaged in promoting teacher professional learning has the knowledge and skills to do these things. For this reason, it is unfortunately possible for professional development to have an adverse impact on teacher practice and student outcomes.”
- “Schools do not thrive on visions alone, so leaders must ensure that professional learning opportunities are well managed and organised and that appropriate conditions are in place for the extended engagement that in-depth professional learning requires. “
- “Regrettably, most efforts to improve student outcomes through professional learning and development are short-lived. For improvement to be sustained, short-term perspectives need to be extended to more distant horizons. Although the research base identifying the conditions associated with long-term improvement is
somewhat thin, one thing does appear clear: sustainability depends both on what happens during the professional learning experience and on the organizational conditions that are in place when external support is withdrawn.”
The results are out for last years NCEA exams. I taught 3 classes of Yr 12 Physics last year (almost 70 kids).
I used a modeling method, and only taught mechanics. We spent far longer on motion graphs, motion maps, understanding differences in acceleration and constant velocity, energy bar charts etc. We spent a lot more time going into much further depth with mechanics, with the hope of achieving understanding, as opposed to memorisation from spending less time on mainly formula plugging exercises.
My FCI data from this year indicated an improvement:
My results are under the abbreviation MCG. The others are from a Hestenes article (Notes for a modeling theory of science, cognition and instruction).
However my NCEA results were interesting.
I have a higher percentage of students receiving Merit and Excellence in the Mechanics paper than in previous years (nearly 50% of the cohort in 2018). This was expected.
But I have a higher number of kids getting a Not Achieved than previous years (~38 %). This was not expected.
Here are my thoughts to try and explain this Not Achieved result:
- Maybe these bottom kids have not done enough independent work themselves through the year (in groups others are doing the work for them)
- In the past my bottom kids still didn’t understand physics, but they had done enough plug-and-chug to pass the test.
- They may have had enough on their test to start a problem/show understanding. For example, on a momentum conservation question, they may drawn a momentum bar chart. But this would be completely new to markers, and not given credit.
My current actions I think I will take are:
- I have significantly cut down the size of the work book I produced. Last year, as the first year, it had far too much stuff, and we didn’t get to do everything. Now we have time to complete everything, and that will be the expectation.
- I choose groups, and we rotate groups every model. Perhaps these bottom students are getting used to the same kids doing all the heavy lifting (thinking).
- Identify these kids in trouble near the end of the year, and give them a simplified version of physics, with the tools and the practice to do plug-and-chug, to give them a chance at passing the exam (although they might not know the physics…).
- Explicit problem solving practice, based on Alan van Heuvelen’s worksheets
- A better revision lead up/homework throughout Term 2 and 3, which includes “interleaved practice”. This could start off by just getting kids to choose the correct model, and not actually solve the problem (so as to reduce cognitive load)
- Be more efficient in class. With being a peripatetic teacher last year, and also having “Monty Python Mondays” etc, as a conservative estimate, I probably lost 10 mins of every class (1 hour). By being more efficient, I can effectively add in an extra period almost every week.
These are my initial thoughts. I would love to get my hands on some papers, and have a look at how these kids did.
Herbert Walberg and Susan Paik
Another article of my summer reading in the “Educational Practices Series” from the International Bureau of Education.
Sections of the paper:
- Parent Involvement
- Graded Homework
- Aligned time on task
- Direct teaching
- Advance organisers
- The teaching of learning strategies
- Mastery Learning
- Co-operative learning
- Adaptive Education
My thoughts/summary/quotes from each section:
- The home environment is vitally important for success in school, so co-operation between parents and educators can support these approaches.
- “[The effect on learning of homework] is almost tripled when teachers take time to grade the work, make corrections and specific comments on improvements that can be made, and discuss problems and solutions with individual students or the whole class”. I think could be a year long project for me one year.
- As a teacher, I need to be efficient in class. “The teacher’s skillful classroom management… increases effective study time”.
- “Six phased functions of direct teaching work well: 1. Daily review, homework check and, if necessary, reteaching; 2. Presentation of new content and skills in small steps; 3. Guided student practice with close teacher monitoring; 4. Corrective feedback and instructional reinforcement; 5. Independent practice in work at the desk and in homework with a high (more than 90%) success rate; and 6. Weekly and monthly reviews”
- “Advance organizers help students focus on key ideas by enabling them to anticipate which points are important to learn”. This section has inspired me to make an advanced organizer which doubles as summary sheet for each physics model. Watch this space!
- The teaching of learning strategies. Not sure I got much from this one.
- “Peer tutoring (tutoring of slower or younger students by more advanced students) appears to work nearly as well as teacher tutoring… Significantly, peer tutoring promotes effective learning in tutors as well as tutees. The need to organize ones thoughts to impart them intelligibly to others… benefits the tutor”. This made me think of a newish idea to try in whiteboarding sessions. When kids don not understand something, go straight to a TPS (think-pair-share) in a group. Im aiming for a a few learning moments before we share it as a group.
- “For subject-matter to be learned step by step, thorough mastery of each step is often optimal”. This section made me really think of standards based grading. Something I still want to get into.
I submitted an article to NZ Science Teacher and was published over the holiday! Here is a copy of the final draft I sent in as they haven’t yet updated their website.
“Id been the coach for the teaching semester, and all of a sudden I’d made this Jekyll and Hyde transition and became the judge [of their assessments]. Would combining the roles of coach and judge be accepted anywhere else in society. I would be considered unethical” ~ Eric Mazur.
And I agree. Such a strange situation to both teach our kids, then judge them on high stakes assessments (internal assessments). I really struggle with this part of the year. I have an inner voice that tries to cloud my objectivity by saying “She is normally a great student, and she tried really hard. She would be truly disappointed in just an Achieved grade”.
I wish I could have thought about this a bit more before the submissions on changing the NCEA system were due.
Wim Van Dooren, Xwnia Vamvakoussi, and Lieven Verschaffel
Another in the “Educational Practices Series” by the International Academy of Education.
I really liked this summary. It made me aware of a number of issues in students reasoning for proportional problems (and the misuse of proportional reasoning when an additive solution is appropriate). It also hammered home that in physics, teachers are probably not aware, but proportional reasoning is one of the foundations of our subject, and it is something either take for granted that the students know, are are unaware of its importance.
Headings in this article are:
- The pervasiveness of proportionality in the mathematics curriculum: An overarching concept
- The importance of mastering one-to-many correspondence
- Acknowledging the validity of a variety of strategies
- Stimulating variety and flexibility in strategy use to develop understanding of proportionality
- Inappropriate additive reasoning is a major source of errors in proportional problems
- Be cautious of the overuse of proportionality
- Improve teacher knowledge
- Concluding educational recommendations
My summaries for each section (or good quotes)
- “Proportionality is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics” (or physics!)
- Proportionality is a “big idea”, that is a connective thread through many topics. “One of the first (implicit) encounters with proportionality is that of measuring quantities, as this relies on the decision to refer to one quantity as the ‘unit’, which leads to a linear relation between the physical quantity measured and the number assigned to it.”
- One-to-many correspondence is also known as “repeated addition” (If I need 4 handfuls of sand for 1 bucket, I will need 4 + 4 + 4 handfuls for 3 buckets). These can be fine, and persist as the main strategy to solve proportional problems, but it can run into issues. “These informal strategies do not necessarily evolve to more sophisticated ones”. However “teaching students formal methods does not guarantee that they will use them when appropriate … On contextualized problems, secondary school students who were taught the formal method of solving the expression a/b = c/x for the unknown have been found to perform worse than completely illiterate adults who never set foot in school”. Really?! Will have to find this study!
- Formal proportional strategies include “within-strategies” and “between-strategies”: For example, for making jam I use 3kg of sugar with 6kg of strawberries. How much sugar is needed for 18kg of strawberries? The within-strategy is comparing the 6kg and 18kg of strawberries (3 times bigger). The between-strategy is looking at the relationship between sugar and strawberries (sugar always half of strawberries). Other strategies are ratios, cross-multiplying and fractions.
- Although we might poo-poo “repeated addition”, because “it is less sophisticated, more limited, but more meaningful for the novice learner”. Conversely “between-strategies are more sophisticated, less limited, but less accessible to the novice learner”. Finally “the strategies of creating equivalent fractions and cross-multiplication have as a major advantage that they are algorithmic in nature. One can follow a fixed and guaranteed accurate procedure… However research points out that students themselves rarely choose them, and mistakes are very common. One of the main causes seems to be that these algorithms consist of the blind manipulation of numbers according to formal rules that have no relation whatsoever with the original problem context.” This section really resonated with me about how I feel physics is often taught, and also I think the authors have really summed up my interpretation of the direct instruction/interactive learning divide in maths.
- Incorrect use of additive reasoning is the biggest source of errors in proportional reasoning. “Task related factors may discourage or enhance additive errors. For example, an important task-related factor associated with fewer additive errors is familiarity with the meaning of the rates (external ratios) involved in the problem (eg speed in kilometers per hour) … furthermore non-interger ratios trigger additive errors. eg When grandmother makes jam she uses 3.5 kg of sugar for 5 kg of strawberries. How much sugar does she need for 8 kg of strawberries.” Being aware of this level of detail is how good our exam writers should be …
- “Much research has shown that students also apply proportional strategies where this is not appropriate” (When an additive solution is more appropriate). It turns out, that like the quote in the section above, the choice of numbers on questions can change the percent of kids who answer correctly. In this case, kids who might mistakenly use proportional reasoning (instead of correctly using additive) will accidentally use the correct reasoning if the numbers picked are non-integer ratios! From answering too many proportional questions kids acquire a “routine expertise”, instead of “adaptive expertise”. “For students to develop adaptive expertise in proportional problems, it is essential that they acquire the habit of explicitly and systematically questioning whether proportionality is the right mathematical model for the situation at hand.”
- “There are clear indications that pre-service and also in-service teachers sometimes struggle with difficulties similar to the ones summarized above. … in-service teachers rely strongly on additive building-up strategies … other studies have also documented that in-service teachers strongly favour the cross-multiplication approach … and often they did not acknowledge the value of any other strategies explained above, and considered them as less sophisticated or even wrong. “
- “Treat proportionality as a “big idea””. Great suggestions here too (consider a modeling approach, teach for adaptive expertise, use a variety of tasks).
Often in physics classes we end up a number of kids who believe that the main part of solving physics problems is finding the right formula: “formula hunting”. This can become very clear when helping a student and all they want to know is “what formula should I use”.
These type of students end up having a very limited, and disconnected view of physics, and struggle to apply physics to the real world. For them, there is the real world, and then there are well written physics problems, in which they only need to find the right formula to solve them. As Hestenes once said “Students are not easily weaned fro a formula-centered problem-solving strategy that has been more successful in the past” (Hestenes, 1987, Towards a modeling theory of physics instruction).
What I would to stress in this blog post is that in New Zealand, our attempt at qualitative questions devolve to formula hunting as well. Very often our “explain” questions are written, so that students can just pick a formula, and use it to explain.
For example, students would typically answer one of these questions with “The formula is A = BC, and if B goes up, A goes up too. C is constant”.
Although correct, it does mean that we are once again putting the almighty formula on a pedestal for our students. Without a doubt they will com away from the course believing that physics, and physics problem solving is based around formula hunting.