If Your Students Find Maths Difficult, Read This!

Alexandra Riley reports on some new research, highlighting five key ways for school leaders to make maths work for both children and teachers.

New analysis suggests that the UK is expected to ‘drop’ three places in world numeracy tables by 2030, with a number of OECD countries set to overtake us.¹

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      string(358) "... he or she prepares to deliver the maths lesson they dread? How discouraging must it be to hear rants at home about the ‘terrible new maths?’ Mathematics has a bad reputation because there are not enough people who truly believe that mathematics is beautiful. Before ever introducing a mathematical concept ..."
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      string(5758) "It’s time for maths. These simple words can cause heart palpitations for the brightest and the best, so imagine what it does for the student who has been told, “You are not a maths person”. What is exciting about taking out a textbook and practicing steps over and over without understanding? Don’t you think students notice the sadness in the teacher’s eyes, as he or she prepares to deliver the maths lesson they dread? How discouraging must it be to hear rants at home about the ‘terrible new maths?’ Mathematics has a bad reputation because there are not enough people who truly believe that mathematics is beautiful. Before ever introducing a mathematical concept, teachers have a lot of baggage to unpack. It is important to kick off the year by letting students express their feelings about the subject. This can be done using a ‘Getting to Know You’ survey and/or having an open and honest discussion around this topic. Students need to know that they can be truthful without penalty, and that this information will be used to help design a maths program that meets their needs. Teachers need to take the time to share their own feelings and a little about their own mathematical journeys. It is vitally important that teachers teach maths from a place of positivity and wonder, even if it is not their favourite subject to teach. Providing an environment where it is safe to take risks and fail is critical to the success of the students. There needs to be a shift from a fixed mindset to a growth mindset in order to foster deeper learning.How do we get students to fall in love with mathematics? Let them be in charge. Cognitively Guided Instruction (CGI) is a student-centred approach to teaching mathematics. Teachers build on what students already know and allow students to rely on their own intuition to approach problem solving. It is a way of using students’ natural number sense to guide instruction and deepen understanding. Teachers serve as facilitators, listen to students, ask probing questions and engage students in discourse and reasoning about their thinking and the thinking of others. Children are given the opportunity to learn from one another and make connections, which helps them to achieve conceptual understanding. Children need to guide mathematics instruction and teach one another. Instead of introducing the algorithm for adding with regrouping, create a story or scenario which requires students solve a problem. Provide a situation that is relatable and realistic, so students think more about solving the problem than adding numbers and following steps. Even younger children without experience with these types of problems will surprise you. If students are allowed to attack the problem without the constraints of an algorithm, they think more creatively and solve problems often thought to be beyond their reach. It is important for students to have access to all types of manipulatives, and that the use of them is celebrated, not reserved for ‘strugglers’. All students should be encouraged to create visual representations and find multiple strategies to show their thinking. Students need an opportunity for productive struggle, so DO NOT rescue them if it gets hard. Encourage them and ask questions that might help them think of different ways to approach the problem. The teacher’s role is to observe the process and make note of strategies that should be shared with the group during the discourse. Children need the opportunity to engage in maths discourse. While it may be tempting to lead a discussion around the great maths thinking you have witnessed, resist the urge to do so. Allow students to present their strategies to the group, while you serve as the scribe. Be precise, recording the strategy as closely to the student’s work as possible, while modelling organisation. Allow classmates to ask questions and take notice of similarities and differences across varied strategies. Students will learn to express themselves clearly, defend their ideas respectfully and be open to new ways of approaching the same problem. Students need to know that there are many paths to the same destination, so they can grow more flexible in their thinking. Soon maths conversations will be happening regularly around the classroom, on the playground and at home. Healthy debate in a safe space builds confidence and sparks curiosity. Students need opportunities to justify and reflect. Often times teachers overlook the benefit of having students reflect in maths class. This is yet another way to solidify understanding. After engaging in maths discourse, students should be given the charge to pinpoint something that clicked for them. Each student will have something they can reflect on, either their own strategies or the strategies of a classmate. They could also write about something new they have learned or a connection they have made. Some students might choose to applaud the work of another student, but push them to explain what intrigued them by using detailed examples. They could also express something that was confusing to them, even if they still don’t understand. Some students might copy the strategy of a classmate, so they can try it next time. In some classrooms, students’ strategies are named after them if they are the first to use it successfully. A wonderful lesson for children to learn that can come out of reflection is that mistakes can be opportunities for learning.Students need the opportunity to examine and critique the work of others. Although they"
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Maths That Make You Smile

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      string(5755) "The headline finding is that far from hindering young maths pupils, using calculators in maths lessons can improve pupils’ calculation and problem-solving skills. The report stresses that, for calculators to be helpful, teachers need to teach pupils how to use them in a thoughtful and considered way. The review finds is that calculators can actually boost pupils’ fluency and understanding of maths – but that to do so, teachers should ensure they are used in a considered and thoughtful way, particularly with younger students. It showed that pupils who had used calculators systematically throughout primary school had a greater understanding of and fluency with arithmetic. However, the report added that primary school pupils should use calculators regularly but not every day. And it said secondary school students should be allowed more frequent access to calculators so they can make decisions about when and when not to use them. 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The effect of formative assessment is more modest, but is more effective when teachers receive professional development or feedback is delivered through computer-assisted instruction. Collaborative Learning (CL) has a positive effect on attainment and attitude for all students, although the effects are larger at secondary.Discussion is a key element of mathematics teaching and learning. However, there is limited evidence concerning the effectiveness of different approaches to improving the quality of discussion in mathematics classrooms. The available evidence suggests that teachers need to structure and orchestrate discussion, scaffold learners’ contributions, and develop their own listening skills. Explicit instruction encompasses a wide array of teacher-led strategies, including direct instruction (DI). There is evidence that structured teacher-led approaches can raise mathematics attainment by a sizeable amount. DI may be particularly beneficial for students with learning difficulties in mathematics. Inquiry-based learning (IBL) and similar approaches involve posing mathematical problems for learners to solve without teaching a solution method beforehand. Guided discovery can be more enjoyable and memorable than merely being told, and IBL has the potential to enable learners to develop generic mathematical skills, which are important for life and the workplace. However, mathematical exploration can exert a heavy cognitive load, which may interfere with efficient learning. Peer and cross-age tutoring appear to be beneficial for tutors, tutees and teachers and involve little monetary cost, potentially freeing up the teacher to implement other interventions. Students’ misconceptions arise naturally over time as a result of their attempts to make sense of their growing mathematical experience. Generally, misconceptions are the result of overgeneralisation from within a restricted range of situations. Misconceptions should be viewed positively as evidence of students’ sense making. Exploration and discussion can reveal to students the limits of applicability associated with the misconception, leading to more powerful and extendable conceptions that will aid students’ subsequent mathematical development. Teaching thinking skills, metacognition and self-regulation can be effective in mathematics. Technology provides powerful tools for representing and teaching mathematical ideas. However, as with tasks and textbooks, how teachers use technology with learners is critical. Concrete manipulatives can be a powerful way of enabling learners to engage with mathematical ideas, provided that teachers ensure that learners understand the links between the manipulatives and the mathematical ideas they represent. The effect on student mathematical attainment of using one textbook scheme rather than another is very small, although the choice of a textbook will have an impact on what, when and how mathematics is taught. Learners generally find algebra difficult because of its abstract and symbolic nature and because of the underlying structural features, which are difficult to operate with. This is especially the case if learners experience the subject as a collection of arbitrary rules and procedures, which they then misremember or misapply. Learners benefit when attention is given both to procedural and to conceptual teaching approaches, through both explicit teaching and opportunities for problem-based learning.Number and numeric relations are central to mathematics. Teaching should enable learners to develop a range of mental and other calculation methods. Quick and efficient retrieval of number"
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Improving Mathematics in Key Stages Two and Three: Evidence Review

28 Mar 2018

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      string(3769) "about becoming a peer tutor and jot them onto ‘Post It’ notes, which we attached to the board. The most common themes were:‘I am scared that I will be put on the spot’, ‘I don’t know all my tables, I might forget when they ask.’‘I’m not good at my tables’ and ‘I might say a wrong answer.’‘What if I teach them the wrong way?’‘I may not be as confident as they are.’Several pupils were worried about being put with someone they didn’t know.One child was worried that others might just sit there and not learnA few children had concerns regarding the behaviour of their potential tutees’ …they might be rude/silly and I won’t know what to do.’We established that their concerns had similar themes and were common to many people, as they embark on new ventures and especially trainee teachers. We discussed possible solutions to some of the issues raised including the many different resources available to help them e.g. themselves, other adults and the games including those using ICT.Together we set some clear ground rules, which included encouraging others; speaking in a positive way and giving some thought as to how their body language conveys messages. I then introduced the idea of Gardner’s Multiple Intelligences and the children had an opportunity to find out in which ways they were ‘Smart’.I asked them to reflect on previous successful learning experiences. Most pupils talked about learning how to master a particular skill in: football, gymnastics and in learning how to swim. I helped them to draw out the different stages of learning, which follow a pattern: why did you learn it? (to get better) How did you learn it? (by watching, talking and doing) Who helped? (often an adult – parent/coach) What helped? (time and practise) How did you feel at the end? (good, pleased, proud etc) To make this more visual, I listed their ideas on a feelings chart – documenting their emotions before, during and after completing any new learning experience.Rosalyn Mark (Learning Innovation Leader) supports local schools in implementing techniques, including: Collaborative Learning, Peer Tutoring and Growth Mindset. References1. http://educationendowmentfoundation.org.uk/toolkit/peer-tutoring/2. Beasley, C. (1997). Students as teachers: The benefits of peer tutoring. In Pospisil, R. and Willcoxson, L. (Eds), Learning Through Teaching, p21-30. Proceedings of the 6th Annual Teaching Learning Forum, Murdoch University, February 1997. Perth: Murdoch University. http://lsn.curtin.edu.au/tlf/tlf1997/beasley.html3. Biggs (1999) in http://www.beds.ac.uk/jpd/volume-4-issue-1/peer-tutoring4. Cohen, P.A., Kulik, J.A., Kulik, C.C. (1982). Educational Outcomes of Tutoring: A Meta-Analysis of Findings. American Educational Research Journal, 19.2: pp. 237 248.5. Damon W and Phelps E (1989) ‘Critical Distinctions Among Three Approaches’ in Peer Interaction, Problem Solving and Cognition: Multidisciplinary Perspectives. Edited by NM Webb New York: Pergamon Press6. Field J (2003) Social Capital, London: Routledge7. Goodlad, S. and Hirst, B. (1989) Peer Tutoring. A Guide to Learning by Teaching, New York: Nicholas Publishing ED 311 0068. Hammond, J., Bithell, C., Jones, L. and Bidgood, P. (2010) ‘A First Year Experience of Student-directed Peer-assisted Learning.’ Active Learning in Higher Education 11, 2019. Hattie, J. (2012) Visible Learning for Teachers: Maximising Impact on Learning: Routledge10. Topping, K and Bamford, J. (1998)‘The Paired Maths handbook; Parental Involvement and Peer Tutoring in Mathematics David Fulton Publishers"
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Creative Teaching & Learning

Can peer tutoring raise achievement in maths?

20 Jun 2017

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      string(2456) "parking lot, we linked the story problems to the popular Isle of the Lost series that is based on Disney fairy tale characters from Disney’s Descendants films.Students used perimeter and area calculations to use maths in a way that really mattered to them. We created story problems to calculate how to unite all the fairy tale kingdoms and plan the space for the island prison to hold all of the villains. Students figured out the area of the Island Prison and the amount of material they would need for the fencing perimeter. They were challenged to decide how many other kingdoms could be comfortably relocated in the Island Prison: Jafar’s Castle, Captain Hook’s boat parking and Ursula’s underwater kingdom. Students were so excited about recreating this magical world, we took it a step further to make tangible maps where they created 3D paper renditions of the kingdoms. They were figuring out the area to redecorate rooms in castles and how much room they could have for each kingdom. The scenarios we presented were based on fantasy, but they were real and important in our students’ worlds. This was the most excited and engaged we had seen them about a maths topic and they took ownership of the lesson by moving into self-directed inquiry.Why it worksIn addition to creating an entry-point and getting students excited about STEM, these projects push students to think of STEM more creatively. In today’s world, technology is changing so quickly that it is not enough to just know the science – it’s also important to be able to innovate and apply ideas creatively. Connecting learning with pop culture helps students see things creatively, create deeper connections and think outside of the box.Dr. Edward Kang, PhD, NBCT is an Education Consultant and Founder and Director of The Laboratory in Chicago, Illinois creating programming to bring imaginary worlds to life through science. He works with teachers, schools and students to improve their growth mindset and experience how maths and science are rooted in creativity and imagination.Amy Schwartzbach-Kang, M.Ed, NBCT is an Education Consultant working with The Laboratory in Chicago, Illinois to bring literature to life using science and creating programs to enhance reading comprehension, critical-thinking, and collaboration skills. Find out more about The Laboratory at www.thelaboratorychi.org"
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Arts-Based Learning

Why Pop Culture needs to be a part of STEM Education

10 Oct 2018

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      string(4394) "achieve the challenge? What space have I provided in the lessons for high achieving students to push their thinking? Effective CommunicationIn order to be mathematicians and chemists, students must be able to “use the language of the discipline to express, represent, justify, and communicate one’s thinking and ideas” (p. 164). In the maths lesson, students had to use thinking routines to document what they already knew about vectors and then share, communicate and justify these ideas to each other. The MicroLab protocol is a great communication tool because it requires students to express their ideas to each other, and since each person has time to talk, those students who normally may not share an idea have an opportunity to express their ideas. Also, when exploring the new concepts, groups had to communicate their ideas to each other in order to answer the guiding question. In chemistry, groups presented their voltaic cells and explained how they work. By explaining their cells, especially the ones that do not look like those in the textbook, both the listeners and presenters are able to deepen their understanding of voltaic cells. When designing lessons that contain effective communication, we find the following questions useful: How much is the teacher talking? How much are the students talking? How are the students given time to share and communicate their ideas? Perceived WorthIn these lessons, students were asked to create a product, whether it is the solution to problems, the construction of a battery or a method to finding a vector. Ron Ritchhart notes, “Production is common in classrooms, but what is not so common is that what is produced is perceived by students to be of value and worth their time and investment” (p. 164). The revised chemistry and maths lessons worked to increase the perceived worth of the products required. In the old chemistry lesson, the required product was solutions to practice problems. These problems have little perceived worth – students understand that their ability to accurately solve these problems will impact their grade, but these problems are largely disconnected from the ‘real world’. In the new lesson, perceived worth was increased by relating the challenge to batteries in cell phones. Rather than just being able to solve problems related to voltaic cells, students are now using chemistry to understand an object they use every day. All the information and understanding that students discovered about voltaic cells related to this challenge, which is what is shown to create perceived worth the most, “….it [is] the ability of the teacher to place the activity within the context of a larger goal or enterprise that mattered” (p. 165). In the maths lesson, the larger goal was the use of unit vectors in particle motion. In the past, unit vectors were treated as a stand alone topic that students learned about because it was in the syllabus. Now, the use of vector notation and finding magnitude paved the way to find unit vectors which paved the way for the application to velocity and motion. Furthermore, by adapting the home thinking to each group’s progress, it placed worth on the thinking and understanding they were doing during the class period. When thinking about increasing perceived worth, I ask myself the following questions: To what extent is this lesson connected to a larger goal or context? How have I made connections to this larger context or goal clear to the students? As we continue to challenge the “..widely held misconception: that teaching is primarily the delivery of information and that learning is memorizing that information” (p. 151), creating powerful learning opportunities is crucial to ensure deep learning. Designing these opportunities is an art and is an iterative, exciting process that can only be improved with careful consideration, time and trial-and-error. Although the new lessons above are richer examples than their predecessors, these lessons will undergo continuous changes as our experiences grow. Jeffrey Watson is a Maths teacher and Roger Winn is a Chemistry teacher at the International Academy East high school in Troy, Michigan, USA. They can be contacted with questions or ideas at jwatson@bloomfield.org or rwinn@bloomfield.org. "
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Cognition and Intelligence

Cultivating a Culture of Thinking

10 Oct 2018

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