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Having undertaken the Lighthouse Maths program as a Year 3 Teacher in 2021, I am fortunate to have been imparting my knowledge of this incredible program as a Lighthouse Maths Coach since 2022. This coaching role involves supporting primary school teachers in their classrooms to deliver effective problem-solving lessons.
The Lighthouse Maths program challenged my initial beliefs and norms regarding mixed-ability groups, lesson structures, questioning and teacher intervention. Embracing the recommended three-phased format of Launch, Explore, and Discuss, I incorporated new knowledge into my mathematics lessons. Throughout my teaching and coaching journey, I have witnessed and experienced transformative changes in delivering powerful problem-solving lessons, particularly around strategic questioning.
Peter Liljedahl’s book, Building Thinking Classrooms*, shed light on the detrimental effects of constantly answering proximity and stop-thinking questions. Instead, focusing on keep-thinking questions allows students to develop their problem-solving abilities and foster a culture of thinking and learning. According to Liljedahl (2020) the average teacher answers between 200-400 questions in a day:
Proximity questions— the questions students ask because you happen to be close by.
Stop-thinking questions— the questions students ask so they can reduce their effort, the most common of which is, “Is this right?”
Keep-thinking questions— the questions students ask so they can keep working, keep trying, and keep thinking.
Liljedahl’s research showed 90% of student-posed questions fall into the ‘proximity’ or ‘stop-thinking’ categories and that answering these is antithetical to building a culture of thinking and learning. “Giving students a thinking task is pointless if we proceed to answer all the students’ questions about how to solve it.” (Liljedahl, 2020).
To improve questioning and deepen students’ thinking abilities, I rephrase my responses to students’ questions by focusing only on answering ‘keep-thinking’ questions. These open-ended questions sound more like:
The pedagogical shift in strategically anticipating student responses and tailoring specific ‘keep-thinking questions’ has been a focus for myself and many teachers new to Lighthouse Maths.
Case Study: Mel Maria Primary School
When visiting Mel Maria Primary School, I worked closely with two teachers to refine their questioning techniques. A notable case study involved posing a problem to Year 3 students about determining the number of squares in a 4×4 grid:
Initially, some of the students thought the answer was simply 16. However, through guided questioning and opportunities for reflection, they were able to arrive at other solutions.
When working in small visibly randomised groups, the teams engaged in discussions, exploring vocabulary such as same lengths, equal, parallel lines, 3D and 2D (due to recent geometry lessons), corners, squares, more, less, and multiplication.
When approaching one group, the conversations between the teacher and student were:
Teacher: “How many squares have you found?”
Teacher: “Are you sure there’s 17?”
Teacher: “Show me”.
Student: (proceeds to point squares) “There’s 4, 8, 12, 16” (skip counting the rows of 4), then plus the big square = 17.
Another student in the group showed the same answer, using a less efficient but still appropriate counting method:
Below, the student counted each square and labelled its position, then added the overall perimeter square to clearly annotate the 17th square. Asking all students to share their working out ensures everyone agrees and understands the squares under discussion.
Teacher: “Remember back to the initial problem, we looked at a much smaller square. How many were there then?”
Student: “5” (remembering the 2×2 grid shown in the Launch).
Teacher: “Yes, but how many different sized squares were there?”
Teacher:Proceeded to state that this square was bigger, hinting at the fact that therefore the size of squares would be greater.
Teacher: “So, will there be more different sized squares?”
Teacher: “How many?”
Student stops and stares at grid.
Teacher: “I’m going to let you think about that now.”
The teacher walks away, leaving the group with a focus: what other squares could be made following the pattern.
Scanning the room, the teacher notices a few groups have come to the same conclusion of 17 and applies similar questioning and enabling prompts to help them realise there are more squares of differing sizes. Meanwhile, another group debated over whether there were 29, 30 or 32 squares…
Teacher: “Explain your thinking”.
Student: “Well, I have dotted the 16 squares. Then, I put a little circle around the other squares”.
Teacher: “What other squares?”
Student: “These ones” (points at 4×4 squares).
Teacher: “How many more squares can you find that are the same shape as those ones?”
Student: Thinks about question and looks at working out.
Teacher: “Oh, I like how you used your way of tracking which squares are where. It makes it very clear. Are you sure there are only 8?”
Student:Looks at working out and realises he forgot about the central 4×4 square.
Teacher: “Very good, what about the bigger circles?”
Student: “I think there are these 4 squares” (points the 3×3 squares out). “But maybe there’s more”.
Teacher: “I want your team to agree on how many squares all up”.
The teacher walks away, encouraging the group to share their answers, identify all the squares, record this working out and justify their total to reach a consensus.
I sometimes refer to these powerful teacher-student conversations as “tennis matches” where questions and answers are volleyed back and forth, moving thinking forward. This type of learning and reasoning is deeply embedded in Lighthouse Maths. Statements like: Is this always true? What conjectures can you make? How can you prove it?
In the final part of the lesson (the discussion phase), students had the opportunity to share their working out and compare differing recording methods. This allowed a deeper understanding of the problem and the ability to identify and correct misconceptions. Students celebrated their efforts and discovered more efficient strategies and recording methods.
Throughout these powerful discussions, students articulated how they overcame challenges, at what point they realised more squares were possible and how they ensured they had found all squares. Upon reflection, the class realised there was a systematic way to identify all the squares, working from the smallest to largest and counting the total amount of each size:
Lighthouse Maths offers a transformative experience in mathematics education, empowering students through strategic questioning techniques. It fosters confidence and resilience as students tackle intricate problems, leading to a deeper understanding of mathematical concepts and their interconnections. This program revolutionises teaching by emphasising productive struggle, critical thinking, and problem-solving, enabling students to excel and teachers to witness remarkable growth.
I believe the magic of this program lies in its ability to engage, connect and transform. I have witnessed firsthand the profound impact on students’ mathematical abilities and mindsets, shaping them into critical thinkers who seek connections and persevere through challenges. Illuminate your mathematical journey with Lighthouse Maths and discover problem-solving in a whole new light!
Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin press.