I write a lot about Harkness and its impact on my teaching and how it makes me think about mathematics but none of that actually matters. What matters is the impact it has on the students and their learning. I thought I would address this with a post based on recent pupil feedback in my year 9 class. The biggest criticism of the Harkness approach is that it won’t work with big groups. I am a staunch opponent of this but I do think things change and educators have to be a little more creative.
Before we carry on, these students aren’t professionals – I do not expect them to know what is the greatest impact on their learning but it is illuminating to ask them every now and then how they feel and what is working. It will certainly effect a few changes in their classroom this term. I also know that pupil feedback is limited because of this (a more in-depth blog on this here) but for the reasons above, let’s see what the group of 13-14 year old mathematicians think of this approach.
The students were asked two questions:
- What has been most beneficial to your learning in your lessons in this subject?
- What would help you to improve your learning experience?
To summarise, after ‘coding’ the verbal responses, students think the ‘discussion’ aspect of Harkness lessons is the most important part of their learning experience. They also believe that seeing and completing solutions on the board is beneficial to their learning.
What do students think of talking about maths?
“Good communication between students”
“I like the way that we express our opinions about other people’s work in a constructive way”
“When Mr. McDonald comes over to explain just to me or my table”
“We get a lot more opinions from the class”
Above are a few of the anonymous comments relating to the discussion aspect of a Harkness classroom. I particularly think point 3 is a great benefit of this approach. There is far more time for student-teacher conversations on a more personal level while others are having a discussion. This gives students an immediate feedback and means I can tailor follow-up questions as much as possible. Secondly, the last quotation is the one I was most surprised with. I had envisaged students complaining that there were too many opinions and I wasn’t letting them know which is right or best or whatever. In fact, this student believes the opposite. I love the use of the word opinion as it shows that this student is happy to challenge and question others. Small groups of four students is nothing new but I really try and challenge myself to be economical with my language. Every sentence I say must be impactful. Every sentence that a student says has to help someone, if nothing else to improve their confidence.
Why do they like working on whiteboards?
“I find it a really good way to learn from our mistakes.”
“I think writing up all the answers on the board is a unique and valuable approach…this leads to good discussion”
Above are the two main positives to come from students’ opinions of the work on boards. To reiterate, students put all solutions to the work completed pre-lesson on the board. Spotting mistakes is framed negatively but I think this is meaning when someone else has got a correct answer. I was disappointed that no students commented on feeling more confident to put solutions on boards as this is something I am really striving for in the classroom. The students will challenge each other and some will put up a different solution next to one that is already up. I encourage students never to rub anything out. The second quotation leads to the discussion we have already mentioned and I like that students recognise the point of putting things on the board. It is not a gimmick and it is not to make us look good. We put things up for everyone to see and critique. This allows me to quickly assess for learning too and I am able to prioritise tables and students.
What do they not like?
“I want to do more work in lessons”
“More teaching from the teacher not all Harkness”
“Focus on one topic then move on”
Here we have the main negative themes from the students. Doing more work can come from one of two things in my experience:
- a really good student might not need to discuss very much
- Students don’t/can’t stretch discussions
The second drawback there is obvious and that is up to me to ensure I have ears all around the room so I can ask high-level questions for groups that have grabbed the concept well while others have. The first point is my biggest issue with the Harkness approach in general. It is really difficult to differentiate for the top-end. I have experimented in the past with student teachers and I will certainly revisit this but I am looking at how we can better do this. I think it is also important that the quality of discussion is monitored and good discussion is championed.
What impact will this have on my delivery?
I will go into this term with a renewed sense of enthusiasm after reading their insight. It certainly highlighted to me how important it is to these students that they have ownership over their learning. I will endeavour to produce more high-end material in class through my own questioning and through big problems related to the current topics. I will also ensure all students are getting involved with discussions and are contributing, whether that is through a solution, a challenge or a question. Harkness can work with a large group of students – it just looks different and the teacher must trust the students to be doing the right thing at the right time.