**What were the main things you discovered about how the pupils learned mathematics?**

We found that overall students really enjoyed the Inquiry based approach to lessons. That is not to say that all students were fully engaged throughout the whole of the lesson; but from observations and student responses it was clear that the majority of students enjoyed the freedom to regulate their own learning and choose what it was they were investigating. The Year 7 students have been exposed to previous Inquiry based lessons. It was clear that each time students were part of Inquiry lessons has developed their higher order thinking skills. Be able to form their own questions and regulate their own learning and develop structured lines of Inquiry. Students ability to work in pairs was also a strong feature of how students responded to these lessons. Many students worked extremely well and surprised us with their maturity and ability to work collaboratively especially when given an A3 sheet to work on together and share their ideas.

**In what ways will this change your teaching in the future?**

We will look to use an Inquiry based approach across all year groups and further investigate how Inquiry lessons could be implemented into the Schemes of Work. This should enable us to better develop not only key subject knowledge across specific topics but also look at developing students high order thinking skills. It has also highlighted the importance of collaborative working and thinking carefully about which students you want to work with each other and why. It is important to look at confidence, ability, and SEN when pairing or grouping students to work independently.

**What were the main things you learned about the pupils that you did not know so clearly before?**

From the very first research lesson the students knowledge of the functionality of a scientific calculator was higher than expected. Many made us of the % button to perform the calculations, something that has not been covered during their time at Highcliffe. Many of the year 8 students did not appear to have the same knowledge. The inquiry based lessons highlighted strengths and weaknesses in students that had not come through during traditional style lessons. It also became clear that many students found it difficult to translate between English language and Mathematical language. The ability to replace words and phrases with mathematical operations and numerical values was a real challenge for students across all three groups. There is a lack of knowledge of mathematical notation and what it really means did hinder some students in their ability to progress through the activity.

**In what ways will this inform your future practice?**

There needs to be an increased focus on developing understanding of mathematical notation and language from the start of Year 7. Increased use of the functionality of calculators could supplement this well as it allows students to perform more complex calculations and be able to visualise and draw conjectures from the results. Questioning during lessons need to encourage students to investigate lines of inquiry such as: What would happen if..?Why is this true..? How do you know..? can you convince me..?

**What other things have you learned about teaching or learning not captured in 1 or 2?**

The way in which an activity is introduced will have a real impact on the progress of students in the lesson. The Inquiry based approach is challenging and risky; to make it work it is vital that there is a clear aim for the lesson. During the final research lesson the starter activity highlighted that most students could not calculate percentage of amounts effectively. This was overcome by introducing the functionality of the calculator, this enabled students to focus on the investigative and exploratory element of the lesson. The aim was to develop metacognitive skills such as monitoring and regulating thinking and not specific content success criteria.

**How will this change your teaching in future?**

Ensuring that lesson objectives are not solely based upon developing mathematical skills but provide opportunities for students to develop how they learn and why to learn in a certain way.

**Are there any implications for the mathematics curriculum, assessment or pedagogy?**

It can be very easy to stay safe and stick to a method of teaching mathematical skills or concepts where the teacher poses a problem, provide the students with means of solving the problem and then providing solutions. This can however restrict how knowledge is transferred and is determined by the teacher, the method of learning and what is to be learned is taken away from the student. This is not to say that this process is completely wrong and it definitely has a place within a mathematics curriculum. This Lesson Study has shown that Inquiry maths must have a place in the mathematics curriculum, not just as a one off but as a repeated process that the students become familiar with. The Year 7 students have gone through 3 Inquiry based lessons and the improvement in the progress, level of independence and ability to regulate their own learning they have made in these lessons has been clearly visible. Students appear to have more confidence, motivation and willingness to explore. This should enable students to better link conceptual learning with the method of learning. The lessons could fit in as a means of Afl prior to embarking on a new topic or to assess students understanding after a topic has been completed. It can also be an excellent means of challenging students and enable the assessment of deep conceptual understanding.

**What key learning will you share with colleagues in school and within the project?**

The most positive aspect of this project is the collaborative nature of the whole process. The time spent on the lesson study has been discussing students learning throughout the lessons and developing the methods of teaching to maximise the impact the lessons had on not only the case students but the whole class. It is truly a shared experience, building the confidence in all the teachers involved in the project and allowed everyone to feel comfortable to take risks and trial new things. We feel that the Inquiry lesson is something that could be successfully implemented across more subject areas than just within maths. We have seen students develop their ability to apply themselves to problem solving, having the confidence to ask questions like wonder what happens if¯ and then structuring a line of Inquiry to try and answer those questions.

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