This episode is special because it is our first episode topic that was suggested by a listener. A huge shoutout to our friend Erick Lee (Twitter handle @TheErickLee) who suggested this great report published by OECD. If you are on Twitter, please give Erick a follow!
Here is the link to the report:
Every three years the OECD administers and publishes the Programme for International Student Assessment, better known as PISA, which evaluates 15 yearold students around the world to determine how well their education system has prepared them for life after compulsory schooling. This test is important because it allows the performance of educational systems to be examined and compared on a common measure across countries. Currently 70 countries participated in the latest PISA.
Ten Questions for Mathematics Teachers… and How PISA Can Help Answer Them is a report that takes the findings from analyses of the 2012 PISA and organizes them into ten questions that discuss what we know about mathematics teaching and learning around the world – and how these data might help you in your mathematics classes right now.
The questions encompass four broad categories:

 teaching strategies
 student learning strategies
 curriculum coverage
 various student characteristics, and how they are related to student achievement in mathematics and to each other.
Each question concludes with concrete, evidencebased suggestions to help teachers develop their mathematics teaching practice.
For the next several weeks, Maggie and I will tackle one new question from this report. Of course, we begin with Question #1: How much should I direct student learning in my mathematics classes?
WHERE DOES MATHEMATICS TEACHING FALL IN THE TEACHER VS. STUDENT DIRECTED LEARNING DEBATE?
For years, the most common teaching strategy has been teacher directed with a small – but vocal – contingent calling for a more studentoriente
d teaching. Which one is better? Unfortunately, it is not a simple “either/or” proposition. It would have been so nice if the data simply said “do THIS and not THAT”. Rather, it is a bit more nuanced.
It depends on the the content and students being taught.
It is a given that most teachers are directly teaching. Studentcentered practices are most commonly used within the context of differentiating instruction. The PISA survey indicates that students may be exposed to different teaching strategies based on their socioeconomic status or gender. Girls reported being less frequently exposed to studentoriented instruction in mathematics class than boys did. Disadvantaged students, who are from the bottom quarter of the socioeconomic distribution in their countries, reported more frequent exposure to these studentoriented strategies than advantaged students did.
The data show that as the instruction becomes more teacherdirected the more student learning relies upon using memorization skills. Conversely, the more studentoriented the instruction, the less students rely upon memorization and are increasingly able to elaborate upon their thinking.
WHICH TEACHERS USE ACTIVELEARNING TEACHING PRACTICES IN MATHEMATICS?
From the Teaching and Learning International Study (TALIS) – a different OECDled survey – four activelearning (studentoriented) teaching practices are identified:
 placing students in small groups
 encouraging students to evaluate their own progress
 assigning students long projects
 using ICT (Information and Communications Technology) for class work.
These practices have been shown by many research studies to have positive effects on student learning and motivation. TALIS data show that teachers who are confident in their own abilities are more likely to engage in activeteaching practices – which is the bottom line, really. If a teacher feels comfortable with the necessary pedagogy, content knowledge, and classroom management, then they will be able to flexibly think about how to teach it in a manner other than direct instruction.
If this doesn’t scream “WE NEED MATH COACHES!!!”, then nothing does.
HOW CAN A VARIETY OF TEACHING STRATEGIES BENEFIT STUDENT ACHIEVEMENT?
As stated above, as the instruction becomes more teacherdirected the student learning becomes more reliant upon memorization. Conversely, the more studentoriented the instruction, the more students are able to elaborate upon their thinking.
The data indicate that students are slightly more successful in solving the easiest mathematics problems in PISA when teachers direct student learning. Yet as the problems become more difficult, students with more exposure to direct instruction no longer have a better chance of success. Students exposed to greater amounts of studentoriented teaching are more likely to solve the difficult problems on PISA.
This means that one teaching method is not sufficient to teach all math problems; teaching complex math skills might require different instructions strategies than those used to teach basic math skills. In fact, rather than succumbing to an “either/or” mentality (or a directinstruction versus constructivist debate), Singapore is using this research to require teachers to use a variety of teaching methods depending on the complexity of the mathematics being learned.
Teacherdirected and studentoriented instruction must work in tandem.
WHAT CAN TEACHERS DO?
So, let’s wrap this up. What are teachers supposed to take from Question 1? Three things…
 Plan math lessons that strive to reach all levels of learners (differentiation)
Make sure each lesson/unit has extension activities for those who can go deeper. (This is the lowfloor/highceiling concept that Jo Boaler talks about.) Offer support for the struggling learner. And provide a variety of activities and roles for students with different abilities/interests
 Provide a mix of teacherdirected and studentoriented teaching strategies
This requires that the teacher move beyond the textbook provided lessons and homework and add new activities to lessons that allow students to work together or use new tools (technology or games).
 Let the difficulty of the mathematics problem guide the teaching strategy.
Reserve your teacherdirected lessons for simpler math concepts and research other strategies for teaching more difficult concepts.
Please read the actual report! Here…