ADVANCED MATHEMATICS FOR FORM SIX – ALL TOPICS

GET BETTER AT MATHEMATICS – PART 2

4. Create a Study Schedule

Creating
a study schedule is one of the most effective steps to understanding how to
become better at math. By planning your study time, you ensure that you
dedicate consistent effort to your math practice, which is essential for
building and retaining skills. A study schedule helps you manage your time
efficiently and keeps you on track to meet your learning goals. Start by
assessing your current schedule and finding time slots that can be dedicated to
studying math. It doesn’t have to be hours at a stretch; even 30 minutes a day
can make a significant difference.

5.
Master the Basic Math Skills

Calculations
involving numbers, sizes, or other measures are considered basic math skills.
These skills include the fundamentals like addition and subtraction as well as
more advanced arithmetic ideas built on them. In addition to mastering
basic math skills, having an experienced math tutor can greatly enhance your
understanding of more advanced arithmetic concepts.  In addition to
mastering basic math skills, having an experienced math tutor can greatly
enhance your understanding of more advanced arithmetic concepts.

6.
Engage with a math tutor

If
your child is struggling with big picture concepts, look into finding a math tutor.
Everyone learns differently, and you and your child’s teacher may be missing
that “aha” moment that a little extra time and the right tutor can provide. It’s
amazing when a piece of the math puzzle finally clicks for your child. With the
right approach, your child can become confident in math — and who knows, they
may even begin to enjoy it.

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1. Some leaders had used technology for testing. For example, pupils took end-of-unit quizzes on laptops, then received their overall score and information about which questions were correct. Pupils were keen to take a test again, motivated to do even better. Although these quizzes cannot check pupils’ reasoning or wider problem-solving, they provide low-stakes practice and precise information about pupils’ component knowledge and readiness to move to the next topic. This kind of system gives pupils and teachers instant and accurate feedback, while almost eliminating teachers’ workload of marking and analysis.
2. Pupils liked frequent, low-stakes (and timed) testing because they could achieve personal bests. In some schools, pupils talked about testing being fun, with friendly class-against-class competition, the use of music and even a big voiceover. Given the frequency of low-stakes testing and pupils’ positive view, it is unsurprising that no pupils talked about fear of national curriculum tests. These pupils were well prepared, due to high-quality curriculums, teaching and practice. There was no notion of teachers putting pupils under undue pressure or expecting them to compare themselves with others. Pupils knew that speed and accuracy of recall (of component knowledge) were important to aim for. They were proud of the amount of work they could complete, the proportion of answers that were correct and being seen to access the difficult task. This was set against a backdrop of a positive culture where mistakes were ‘OK’.
3. Leaders often used summative tests to compare pupils with the national average and to carry out question-level analysis. Where this was due to a focus on national curriculum tests in Year 6, for example, leaders wanted to make sure pupils were going to be successful. However, there was little consensus about whether leaders had identified mechanisms for understanding the cause of pupils’ lack of progress. Most schools used end of key stage tests, or similar papers. The most positive approaches kept things ‘low key’ and avoided repeated summative testing to ‘show progress’. However, there are still limitations to this approach. Question-level analysis of summative tests does not accurately pinpoint gaps in pupils’ component knowledge. Further, meeting age-related expectations (around 50% accuracy) does not assure leaders that pupils are ready for key stage 3. This is because the subject is hierarchical: new and increasingly abstract concepts integrate, and therefore depend on, mastery of foundational concepts. It is also possible that, because resources are limited, prioritising ‘cusp’ groups comes at the expense of pupils who need support the most.

Systems at the school level

Summary of the research review relevant to systems

School-level systems strengthen the consistency of a pupil’s journey to proficiency. They include monitoring approaches, staff training, resource allocation, teaching and learning expectations, ways of raising the subject’s status and ways of sharing information between stakeholders. Professional development should be a planned and purposeful pathway to expertise in teaching and subject leadership.

4. A well-established culture of collaboration has strengthened and extended networks of support. Leaders across different schools and phases often collaborated on curriculum progression, moderation, supporting professional development and sharing good practice. Larger organisational structures, such as the Maths Hubs and academy trusts, helped to ‘cross-pollinate’ information about high-quality mathematics education. Collaboration and information-sharing extended into staff meetings, leaders’ work to support children’s transition into Year 1, team planning and team teaching. Teachers appreciated opportunities to observe each other, and gained confidence in teaching outside their ‘comfort zone’. This collaboration is positive for pupils’ education and, to use a common safeguarding phrase, results in a large and interconnected ‘team around the child’.
5. Professional development provided by the Maths Hubs and information produced by the NCETM have informed leaders about high-quality mathematics teaching. This knowledge could reduce their vulnerability to quick-fix approaches or unevidenced ‘fads’. This, in addition to choosing or creating high-quality curriculums, appeared to be the key driver of improvement in mathematics education. This is very different from the situation we identified a decade ago, when the ‘Mathematics: made to measure’ report stated, ‘Very few schools provided curriculum guidance for staff, underpinned by professional development that focused on enhancing subject knowledge and expertise in the teaching of mathematics, to ensure consistent implementation of approaches and policies.’
6. These combined aspects were highly positive, signalling a shift away from a culture of high-stakes lesson observations (used, in isolation, for accountability purposes) and planning scrutiny. Senior leaders made sure that subject leads had time to look at books, visit lessons and speak with pupils. Lesson observations were typically frequent, collaborative and low stakes. As teachers at one school told us, ‘Nothing is sprung on us’. Leaders used their knowledge of high-quality mathematics education, rather than the teachers’ standards, to inform observations. They would cross-check lessons with curriculum plans and check for consistency. Rather than generic approaches, they generally looked for features such as modelling vocabulary, using resources, recapping knowledge and supporting pupils with SEND. Feedback to individual staff and at staff meetings gave small, sequential development points to gradually improve teaching and teachers’ understanding of progression.
7. The balance of observations, however, appeared to be weighted more towards what teachers were doing, than pupils’ understanding, focus and practice. This may be because leaders relied on a checklist of observable ‘features’ of teaching[footnote 3]. It is possible that a stronger focus on pupils would give leaders more information about pupils’ understanding, and the variation in type and amount of pupils’ practice.
8. Most primary schools are small, which means that classes are typically of mixed attainment. Occasionally, some year groups appeared to have higher-than-average proportions of pupils with SEND. This presented resourcing and teaching challenges to leaders and teachers. In some schools, leaders allocated experienced and knowledgeable staff to the pupils and cohorts with the greatest needs. In some schools, children with significant SEND would receive their mathematics instruction as a separate group.
9. In Year 6 and, to a lesser extent, Year 2, setting and smaller class sizes were relatively common. This indicates that, despite strong curriculums and teaching, not all pupils are making good progress. It was rare to hear of this approach being used with other year groups. It is likely that allocating more resources to the final year groups leaves little or no capacity to take the most proactive approach possible: to significantly intervene with the younger pupils, closing gaps right from the start.
10. In many schools, pupils spoke highly of the way that their school celebrated and encouraged mathematics. Pupils were immersed in a supportive culture that reduced anxiety and increased their confidence. Hard work, progress and achievement in mathematics were often celebrated in assemblies. Common approaches to encouraging friendly competition and celebrating pupils’ successes were set in a context in which teachers helped pupils to understand why they made mistakes and that it was ‘OK’ to make mistakes. Wherever competition was mentioned, it was framed positively. For example, schools offered pupils opportunities to compete on online platforms or against other schools within a trust, similar to a sports tournament.
11. In many schools, leaders often shared information with parents. This included facilitating workshops, games sessions and interactive lesson observations. Parents would learn about age-related expectations, end-of-key-stage-2 tests, mathematics teaching, and how they could help their children at home. In some schools, leaders invited parents to share the ways mathematics helps them in their jobs. Leaders often signposted parents to useful websites and apps that would help their children.
12. When school leaders were held to account by governors and senior trust leaders, challenge was often based on important, reportable data. This is understandable, given the high-stakes nature of accountability. Governors and trust leaders also visited schools regularly to learn more about pupils’ experiences. However, summative assessment data does not necessarily give senior leaders enough assurance about the level of younger pupils’ proficiency. For example, it is possible for younger pupils to obtain correct answers, but this might mask a reliance on using fingers to count. Governors and trust leaders could easily identify gaps in foundational learning through simple checks, similar to checks of pupils’ phonics knowledge, and then discuss them with senior leaders.

Secondary

Curriculum intent: identifying what pupils need to know and do

Summary from the research review

The curriculum should identify and sequence declarative, procedural and conditional knowledge so that pupils’ knowledge builds steadily over time. Linked facts and methods should ideally be sequenced to take advantage of the way that knowing facts helps pupils to learn methods and knowing methods helps them to learn facts. Declarative and procedural knowledge can be combined and taught as strategies for problem-solving. A well-sequenced curriculum, systematic teaching and opportunities for practice help pupils to become proficient in mathematics. This leads to success and motivation in the subject.

Curriculum design

65. In just over half the schools visited, leaders considered their mathematics curriculum as a 5-year programme. Their curriculum did not distinguish between key stage 3 and key stage 4. This approach ensured that what pupils studied in key stage 4 built on what they had learned in key stage 3.
66. In a small number of schools that had distinct key stages 3 and 4 curriculums, the key stage 4 curriculum for many pupils who were expected to sit the foundation tier GCSE papers repeated all, or most, of what they had learned at key stage 3. This was often because leaders treated examination specifications as the curriculum and ‘started at page 1 of the specification’. They did not design a key stage 4 curriculum that built on what pupils already knew and could do at the end of key stage 3.
67. A minority of schools had a 2-year key stage 3. This often led to pupils being rushed to complete the content of the key stage 3 national curriculum by the end of Year 8. As a result, some pupils’ learning was insecure. This meant that topics had to be retaught in key stage 4.
68. In a very small number of schools, the key stage 3 curriculum was designed around projects or themes. Typically, the mathematics that pupils learned through each project was not clearly defined. Decisions about what mathematics to focus on in each unit were left to individual teachers. At the end of Year 9, pupils in these schools had very varied mathematical knowledge, depending on the combination of teachers they had been taught by over key stage 3. As a result, key stage 4 was mainly spent ‘identifying and filling gaps’ in pupils’ knowledge.
69. In the majority of schools visited, decisions about GCSE tiers of entry were, in practice, taken at the end of Year 9, based on levels of attainment at that time. These early decisions determined the curriculum that pupils would study in key stage 4, rather than what pupils knew and could do at the appropriate stage of Year 11. This limited the mathematics that some pupils learned.
70. One of 2 scenarios was likely for pupils judged to be on the border between foundation and higher-tier classes. If they were placed in a foundation-tier class, they tended to progress through the foundation-tier content at a slower rate than they were capable of, or they would complete their mathematics learning up to a year before their GCSE examinations. If they were placed in a higher-tier class, they were expected to rush through the higher-tier curriculum in the hope that enough content would ‘stick’ for them to be able to pick up lots of ‘method marks’ in their GCSE exams. Both of these approaches denied pupils the opportunity to securely learn mathematics that would be useful in their future study and beyond. Mathematics leaders identified that pressure from pupils, parents and senior leaders to ‘finish the course’ was a significant factor in their decision to design their curriculums in this way.
71. A minority of schools, typically those with historically poor outcomes in mathematics, designed their mathematics curriculum to finish at the end of Year 10. In these schools, pupils spent most of Year 11 in a cycle of completing past GCSE papers, often under examination conditions. Teachers marked the papers and identified ‘gaps in knowledge’. Teachers then re-taught the topics in which pupils had performed less well, focusing on question formats likely to be used in examinations. This approach reduces mathematics education to an exercise in preparing pupils to pass an external examination and does not provide pupils with a rich mathematical education. Leaders in these schools rarely considered why pupils had these gaps in knowledge or whether GCSE assessments were the best way of identifying them. They did not consider whether fewer gaps would exist if pupils were not rushed through the curriculum to finish new learning by the end of Year 10.
72. A minority of mathematics leaders designed their key stage 4 curriculum to maximise the amount of mathematics that each pupil would learn securely. They made a clear distinction between curriculum design and examination specifications. Their curriculums focused on ensuring that pupils finished Year 11 with as much secure mathematical knowledge and understanding as possible. Decisions about which tier of examination each pupil would sit were taken as late as possible. In these schools, some pupils sat the foundation-tier papers despite having securely learned some mathematics beyond the foundation specification. Others sat the higher-tier papers despite not having studied the entire higher-tier specification. This approach better prepared pupils for further study and work, as they had a greater breadth of secure mathematical knowledge.

Example of stronger practice:

Leaders in one school had worked with local post-16 colleges to identify the important mathematical knowledge that pupils might need to be successful in a range of post-16 courses. Leaders used this information to inform their curriculum design for ‘intermediate’ pupils whose learning would extend beyond the foundation-tier specification but not complete the higher-tier specification. This supported pupils to be successful in their post-16 study.

73. Almost all schools visited had curriculums that developed learning sequentially. Leaders had ensured that pupils learned the necessary prerequisite knowledge before beginning to study new mathematical content.
74. All schools had some classes that were split between 2 or more teachers. In some, this was due to timetabling constraints. In others, it was to make sure no classes were taught entirely by non-specialist teachers. Year 7 classes and lower sets in other year groups were disproportionately likely to be taught by more than 1 teacher.
75. Most schools visited had thought carefully about pupils’ progression through the curriculum when they were taught mathematics by more than one teacher. In some schools, different units or curriculum strands were allocated to different teachers. In others, the teachers taught sequentially, with one teacher ‘picking up where the other left off’.
76. Where teachers taught different units or curriculum strands, learning was most successful when leaders had made sure that pupils were not taught new mathematics that required knowledge that their other teacher had not yet taught. When this was not the case, and when teachers did not identify gaps in pupils’ knowledge, pupils struggled to learn new mathematics.
77. In schools where teachers taught sequentially, new learning was less successful when teachers and leaders did not make sure accurate information was shared between teachers after each lesson.
78. A minority of mathematics curriculums explicitly took account of what pupils were learning in other subjects. In these schools, mathematics and other subject leaders had worked together to agree, where appropriate, common approaches to teaching and applying mathematics. For example, in one school, the mathematics leader and science leader had worked together to make sure that the approach to rearranging formulae was consistent across both subjects. They made sure that the examples and exercises used in mathematics drew on formulae that pupils would study in science.

Declarative knowledge (facts) and procedural knowledge (methods)

Summary from the research review

The curriculum should identify and sequence key facts, formulae, concepts and vocabulary. This helps pupils to avoid relying on derivation, guesswork or looking for clues.

There is a difference between methods that help pupils to understand concepts and perform mental calculations and methods that are efficient and useful now and in the next stage of learning.

The curriculum needs to sequence the teaching of mathematical methods carefully. It should allow for some early methods, such as parsing, derivation and complex diagrams, to fade over time (designed obsolescence). Pupils should learn the most efficient, systematic and accurate mathematical methods, so that they can use them for more complex calculations and in their next stage of learning.

79. In the majority of schools visited, leaders explicitly considered the important mathematical vocabulary that pupils were expected to learn at each stage, when designing the curriculum. Making this explicit ensured that teachers developed and checked that pupils were using mathematical vocabulary accurately.
80. In most lessons visited, teachers carefully and consistently modelled the use of correct mathematical terminology and expected pupils to use it when talking or writing mathematically. On the few occasions when teachers did not use vocabulary accurately, for example referring to the ‘bottom of a fraction’ when talking about the denominator, many pupils also failed to use accurate mathematical terminology when talking about mathematics.
81. Teachers consistently emphasised the importance of pupils presenting work carefully so that others could follow lines of reasoning. In some cases, they presented this as important ‘so that you can get method marks in the exam even if you make a mistake’. However, more often, teachers emphasised the fact that mathematics is ‘a communication subject’.
82. When new mathematical procedures were being taught, modelling of high-quality mathematical presentation for pupils was common. Pupils were then expected to present their mathematics similarly. This explicit teaching of accurate mathematical presentation increased the likelihood of pupils communicating their mathematical understanding clearly.
83. In schools where teachers modelled inaccurate mathematics (for example ‘stringing equals signs’: 3/5 of 60 = 60 ÷ 5 = 12 x 3 = 36), similar errors were seen in pupils’ work. Leaders ascribed such errors to gaps in teachers’ subject knowledge.
84. The majority of schools had identified core mathematical methods and approaches that they wanted pupils to be taught at the various stages of their learning journey. Most focused on selecting methods and approaches that were:

‘forward facing’, in that future learning would build on them

‘backward facing’, in that new learning was deepened because it built on what pupils already understood

85. In these schools, the teaching of mathematical methods and techniques was carefully sequenced so that all pupils learned more mathematical knowledge, irrespective of the combination of teachers they were taught by. Leaders in these schools saw the range of mathematical methods to be taught, and the order in which they are taught, as a curriculum decision.

Example of stronger practice:

One school had identified that pupils would initially be taught to expand and simplify pairs of brackets using the ‘grid’ approach. This had been selected following extensive discussion in departmental meetings. It was chosen because it:

built on pupils’ existing knowledge of multiplication of numbers using the grid approach

was extendable to more complex situations, and would, ultimately, support pupils to expand brackets without the need for drawing out grids

86. In a minority of schools, the choice of mathematical methods taught was seen as a teaching decision. The goal was that pupils would be able to answer questions of a specific type. This sometimes led to ‘cul-de-sac’ approaches being taught, which could be used to solve questions of the precise type identified in the curriculum for this year, but were not extendable as pupils developed mathematically. This risks pupils seeing mathematics as a collection of unconnected algorithms to be memorised and applied in specific situations. In these schools, pupils were often taught a range of methods and approaches, but no links were drawn between them. The range of methods and approaches taught, and the order in which they were taught, were not picked carefully to deepen understanding. Instead, a range of methods were taught in the hope that one or more would ‘stick’. In these schools, leaders and teachers were more likely to talk about choosing approaches that enabled pupils to answer examination questions or gain method marks, rather than to develop their understanding.

Example of weaker practice:

In one school, the curriculum aims were identified as ‘I can do’ statements, for example: ‘I can expand and simplify a pair of brackets of the form (ax + b)(cx + d)’. Decisions about the mathematical method(s) to be taught were left to individual teachers. Some teachers taught pupils to complete questions of this type using the ‘FOIL’ mnemonic (‘First. Outside. Inside. Last’). This standalone approach to multiplying a pair of brackets did not build on pupils’ existing knowledge of multiplication. It did not support their future learning, for example being able to expand and simplify expressions of the form (ax + by + c)(dx + e).

Example of stronger practice:

Mathematics leaders in a middle school had worked closely with first schools and high schools in their area to ensure that the methods and approaches they used with children were consistent and coherent as pupils made progress in mathematics. In particular, the schools worked together to explore how bar models could be used effectively to teach new concepts throughout pupils’ mathematics education. The curriculum made explicit how bar models should be used. This ‘joined-up thinking’ ensured that pupils’ mathematical progress did not slow at points of transition between schools.

87. When the choice of method was left to individual teachers, inappropriate methods were sometimes taught. This happened when teachers were not aware of ‘what comes next’ (including education beyond the age range of the school) or ‘what came before’ (including education before the age range of the school). This was because they lacked knowledge of the curriculum beyond the current year group or key stage.
88. A few leaders and teachers identified that high-stakes accountability of internal and external assessments led to them teaching ‘tricks’, such as ‘keep, flip, change (KFC)’ for dividing fractions, that taught pupils to answer questions of the specific type likely to come up in assessments but did not prepare them for future learning. These approaches often led to pupils viewing mathematics as a list of unconnected methods to remember and apply.

Conditional knowledge (strategies)

Summary from the research review

Pupils should be able to recall facts and methods to some level of automaticity before using them for wider problem-solving. The curriculum should reflect this optimal sequencing.

‘Problem-solving’ is not a generic skill, and pupils cannot become problem-solvers by imitating the activities of experts. Pupils need to learn strategies and the most useful combinations of facts and methods to solve types of problem. Since it is not possible for pupils to encounter every possible problem, a suitable curriculum identifies strategies to solve a range of problem types (topic-specific).

89. All leaders said that their curriculums were designed to match the national curriculum aim that ‘[pupils] can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions’.
90. In the majority of schools, leaders said that problem-solving was integrated within their curriculum and pupils were taught to apply new facts and methods to solve problems within each unit of work. In most of these schools, however, teachers were given little guidance on the types of problems pupils needed to be taught to solve in the unit of study. There was no common understanding of how to teach problem-solving effectively.
91. In most schools, decisions about teaching problem-solving were left to individual teachers. This often led to lack of fairness. Some classes benefited from considerable teaching of how to solve structurally similar problems using recently taught facts and methods. Other classes had very little. This lack of teaching was disproportionately an issue in lower sets, and in classes taught by less experienced or non-specialist staff.
92. In some schools, pupils were not explicitly taught how to apply the mathematics they had recently learned to mathematical problems. Their only exposure to solving mathematical problems was through answering the final few questions of a predominantly procedure-focused exercise. Often, many pupils did not reach this stage of the exercise. These pupils, therefore, had very little experience of applying mathematical methods beyond routine and established applications. Pupils in these schools were notably less confident when solving mathematical problems.
93. In a minority of schools, problem-solving was explicitly planned into the curriculum. Teachers understood the importance of demonstrating how to apply mathematical methods to problems and giving pupils multiple opportunities to practise applying these methods to structurally similar problems. In the most successful lessons, teachers clearly ‘drew out’ the similarities between problems to help pupils identify the mathematical techniques that might be useful for different types of problem.

Example of stronger practice:

One department had clearly identified the range of problems that they wanted pupils to be able to solve at various stages of the curriculum. In lessons, teachers modelled how pupils could use new learning to solve mathematical problems. They drew out the mathematical similarities in a range of problems that, on the surface, looked unlinked. They gave pupils opportunities to practise solving problems of a mathematically similar nature.

Meeting the needs of pupils

Summary from the research review

A well-sequenced path to proficiency, with the small steps identified, is important for all pupils and crucial for pupils with SEND. It helps pupils to keep up, minimising the need for catch-up support. Many pupils with SEND benefit from explicit, systematic instruction and from practice in rehearsal of declarative and procedural knowledge. They may also need more time to complete tasks and opportunities to practise, rather than different tasks or curriculums.

94. In all schools visited, teaching assistants supported classes in which some pupils had SEND. It most cases, they supported individual pupils or small groups of pupils in the classroom. A small number of schools used teaching assistants to support the work of the wider class, potentially following teacher-led whole-class instruction, while the teacher provided additional support to the pupils with SEND.
95. Teaching assistants who were working directly with individual pupils with SEND were most successful in supporting mathematical development when they had a secure knowledge of the mathematics curriculum and of the range of pedagogical approaches being used by the teacher. In these cases, it was common for the teaching assistant to be assigned to work mainly within the mathematics department, effectively as ‘a mathematics-specialist TA’, or for the teaching assistant to have received mathematics-specific CPD that focused on the curriculum and appropriate choices of teaching method.
96. Teaching assistants who did not have this specialist knowledge were sometimes restricted to supporting pupils in more generic ways. For example, they offered encouragement or repeated the teacher’s explanations. In a very small number of cases, the teaching assistant’s lack of mathematical knowledge actively hindered pupils’ progress. For example, one teaching assistant advised pupils of ‘tricks’ to follow rather than explaining the mathematical methods the teacher intended.
97. Almost all schools visited structured their classes in sets based on current attainment, at some stage of the pupils’ journey through school. Most had school timetables that allowed pupils to move between sets during the school year. A small minority of schools had explicit systems in place to support pupils who moved from one teaching group to another. For example, they provided interventions to close any gaps in knowledge between the pupil who was moving and their new class. This enabled pupils to be more successful in their new group.

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So many people struggle with mathematics that there’s a term for the dread you feel when faced with a calculation: math anxiety. But the good news is, math doesn’t have to be scary.

Dr. Lindsey Daniels (she/hers), an assistant professor of teaching in the UBC department of mathematics, has some tips for high school and beyond to help students overcome their fear of fractions and succeed in the classroom.

What is math anxiety?

Math anxiety is a the very real feeling of tension and discomfort that interferes with the manipulation of numbers and the solving of math problems in a wide variety of situations. People can experience it from calculating a tip in a restaurant to converting measurements in baking. Math anxiety can contribute to ‘affective drop’, where students experience a drop in math performance due to their working memory being overwhelmed while performing a mathematical task.

Math has a reputation for being difficult. While math can be challenging, it hones our critical thinking skills and teaches us a framework for approaching and solving problems.

What are some tips for students?

There’s no silver bullet because everyone’s experience with math anxiety is different, and so everyone’s strategies will be different. And, those strategies might differ over time too! Having said that, some helpful general tips are:

Find a study strategy that works for you, whether that’s summarizing the key points from every lesson and then doing practice problems, completing a practice test and focusing on areas where you felt less confident, or the Pomodoro Technique of 25 minutes of studying with a five-minute break, to name a few.

Self-affirmation questions like ‘What’s one thing you’re proud of this term?’ or ‘Why is problem solving important to me?’ can be helpful to boost confidence and highlight how far you’ve come. If you find it helpful, ask them often, even every day. Attitudes towards math, including self-confidence, can be a huge contributor to success.

Connect with other classmates and make use of on campus resources. In an upcoming paper, we found university students who were encouraged to utilize additional math resources reported more positive experiences when asked to complete a self-affirmation exercise before their final exam.

When it comes to test time, it can be helpful to simulate the test environment. If it’s a one hour test, start a timer, clear all distractions away, sit down, and do the full practice test. You gain experience in a low stakes way, and you get used to having to sit with no distractions for an extended period of time. This also means on test day, it’s not as big of a shock to the system.

How can parents help?

One good tip for parents is to have a positive attitude towards math in their home and to normalize seeking help. Younger students, particularly those in elementary school, can be influenced by parental beliefs and expectations towards math, including when it comes to gender stereotypes.

Parents can also provide a supportive learning environment at home, particularly for math. A couple of examples that come to mind are telling children, “I see how hard you’re working”, “It’s okay to ask questions”, and “You haven’t mastered this yet, but I know you will”.

For parents that might be uncomfortable with math or providing math support to their children, having some additional resources on hand can be helpful. There are some good online resources available including the Centre for Education in Math and Computing and Khan Academy (although the latter follows the U.S. education system). Parents can also ask if they can watch together and learn along with their child.

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10 Tips to Help Students to Succeed in Math

Tips to Help Students Succeed in Math: Boost their confidence and skills with these effective strategies for math success. Discover practical and fun tips today!

It’s no surprise that math is perceived as a nightmare for many children nowadays. Mathematics is crucial for education, as it cultivates a different thought process in children. Nonetheless, educationists and tutors noticed numerous children experience panic and difficulty with math when faced with problems.

Math can be challenging for many children, but it doesn’t have to remain that way. Help your children find a love for math and make learning fun with the right techniques. Figuring out why your child finds math challenging is crucial for finding ways to make the subject more enjoyable for them

Why Do Some Kids Face Challenges in Learning Math?

Mathematics is a broad field with several sub fields. The more important ones include probability, statistics, geometry, algebra, and arithmetic. Students study a broad range of mathematical subjects at school.

Basic arithmetic, which covers addition, subtraction, multiplication, and division, is among the first topics kids are taught. Still, a lot of people find it challenging to understand these ideas. Why do some students experience this?

Let’s explore the reasons behind why some students struggle with Math:

Some Lack Basic Math Skills and Comprehension

To lay a solid foundation in math, it is essential to comprehend addition, subtraction, multiplication, and division. Children need to initially develop a solid understanding of the fundamentals of math to understand mathematical concepts later in life.

Math Is Often Misunderstood as Just Numbers

Certain kids may find algorithms, computations, equations, and numbers dull and uninteresting. This is because it is unrelated to their daily lives and may be too complicated for them to understand. It helps to convey the ideas and concepts of math pleasantly and interactively to increase students’ interest in the subject.

Some Find It Hard to Remember

For children who need help with math, it might be difficult to retain important formulas and rules, which makes solving problems seem difficult. For those who learn best visually, understanding mathematics, symbols, and numbers may provide challenges. Teaching kids how to solve problems through meaningful real-life scenarios is one efficient technique to deal with this issue instead of having them memorize steps.

Some Children Fear Learning Math

Kids who suffer from math anxiety feel tense, anxious, and anxious when they have to solve mathematical problems or deal with situations that need computational thinking. Math anxiety is common in children and can be caused by a variety of reasons. Certain children may find math topics difficult, which can lead to them falling behind their classmates and feeling inadequate and frustrated. Some people may be reluctant to try math again due to bad experiences from the past, such as being in trouble or receiving punishment for errors.

How to Boost Your Child’s Math Skills?

Selecting the most effective techniques for your child to quickly learn math can be challenging, given the growing number of learning theories and teaching methods. If you want to enhance your child’s math skills, follow these steps.

Establish a Positive Environment For Math

It’s critical to foster a favorable attitude towards math at home. Encourage your child to have a curious and confident attitude towards math. Children pick up on our attitudes, so while discussing math, it’s better to highlight its positive aspects. Instead, stress the value and excitement that comes with learning math.

Collaborate with Teachers

Staying in touch with your child’s teachers is essential for supporting their learning effectively. Regular communication allows parents to understand classroom expectations, teaching methods, and areas where the child may be struggling. By sharing observations from home, parents and teachers can work together to create strategies that reinforce learning and address challenges promptly. This collaboration ensures consistency between home and school, helping the child feel supported in every environment. Active involvement also shows the child that their education is valued, boosting motivation and confidence, and fostering a stronger parent-teacher partnership for academic success.

Don’t Focus On Speed

Never focusing on speed is one way to help your kid excel in math. The method that helps many of the best mathematicians in the world succeed is to tackle problems slowly and deeply. Time restrictions might cause people to hurry tasks, which can lead to anxiety and a false impression of what it takes to excel in mathematics.

Practice Regularly

The key to comprehending arithmetic topics is regular practice. Even if your child doesn’t have homework assigned, encourage them to practice math problems regularly. Practice can be made more interesting and fun by using math games, apps, or flashcards.

Make Math More Enjoyable For Your Kid

Learning math is often frowned upon by people, including kids. Overcome this challenge by making the process of learning math enjoyable. One simple solution to developing your child’s math skills is using educational games and activity books. If you’re looking for a way to cultivate your kid’s curiosity while having fun, Math Puzzles are a fantastic choice.

Use Real-World Examples

Teach your child the importance of math by showing them real-life applications. Encourage them to participate in math-related activities, such as measuring ingredients while cooking or estimating travel time and distance while planning a trip.

Prioritize The Process Over The Response.

Before answering, ask your child to explain how they arrived at it first. While discussing the solution, you can assist your child in identifying their error if they have made one. If your child gave the correct answer, engaging in a discussion will further strengthen their comprehension of the math problem as well as the mathematical formula employed.

Set Realistic Goals

Make sure the goals you set for your child are both realistic and attainable. To make things easier to handle, try breaking things down into smaller steps. Reward them with praise and acknowledgement for their achievements. Setting goals offers your kids structure and direction, which keeps them focused and organized.

To improve your children’s math skills, cultivate their love for the subject. It’s best not to push your child too hard when it comes to solving challenging math problems. Enhance children’s understanding of basic math by incorporating flashcards, math puzzles, and memory games into your teaching methods. It is advised to apply math skills in real-life scenarios rather than limiting oneself to textbook problems.

Conclusion

To help your child excel in math, it’s crucial to work together, establishing a positive atmosphere, adapting to their unique learning preferences, and equipping them with the resources and guidance they need. These tips will enable you to support your child in building the essential skills and confidence required for excelling in math. At TIST we offer training for students to excel seamlessly in all subjects. For more tips and tricks.

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What does it take to improve student success and interest in math? The Philadelphia-based Society for Industrial and Applied Mathematics (SIAM) asked more than 400 U.S. high school math teachers for their advice related to teaching and learning mathematics.

“The good news is that students can have success in math class with the right effort, attitude, and behavior, regardless of a natural affinity or being ‘good at math,’” said Michelle Montgomery, project director of the MathWorks Math Modeling (M3) Challenge at SIAM. “Using quantitative skills to solve real, open-ended problems by employing the mathematical modeling process is a great way to get started.”

The teachers surveyed were all coaches of student teams that participated in the M3 Challenge, a national, internet-based contest with no registration or participation fees. Thousands of high school juniors and seniors spend a weekend in March coming up with a solution to a real-world problem using mathematical modeling. To add a bit of pressure, when the students download the problem, they have only 14 hours to work on it. The 2018 event was the 13th annual contest.

What the Teachers Recommend

1. Build confidence. More than two-thirds of respondents (68 percent) cited lack of confidence as a problem that prevents their students from succeeding in mathematics.
2. Encourage questioning and make space for curiosity. Sixty-six percent of respondents said their best piece of advice for students looking to do well in math was to not only pay attention in class but also ask for clarification when they need to better understand something.
3. Emphasize conceptual understanding over procedure. Three out of four respondents (75 percent) emphasized that working hard to understand math concepts and when to apply them versus simply memorizing formulas is essential to doing well.
4. Provide authentic problems that increase students’ drive to engage with math. Sixty-three percent of participants pointed to students’ desire, initiative, and motivation to succeed in math as being critical, and the majority of them (80 percent) said that applying math to real-world problems helps increase both student interest and understanding.
5. Share positive attitudes about math. Teachers suggest that parents avoid talking negatively about math, and especially avoid saying that it is hard or useless (74 percent)—instead they should encourage their kids not to give up, and help them find math mentors when they’re not able to answer questions (71 percent).

It’s no coincidence that these teaching practices are a regular part of facilitating math modeling. Through modeling, students tackle relevant, authentic, real-world problems. According to Lauren Tabolinsky, academic program manager at MathWorks, making math relevant for students and careers is the reason MathWorks sponsors the M3 Challenge.

SIAM’s Montgomery adds that “inherent in modeling work are things like motivation, identification of variables that affect the issue (no spoon feeding of data or approaches), gut checking of answers, and justifying solutions offered. The result? Interest and enthusiasm for working a problem, and the understanding that being able to use skills in your math toolbox can provide insight into relevant issues facing communities and the world today.”

For example, the 2018 M3 Challenge problem was called “Better ate than never: Reducing wasted food.” Students addressed an issue identified by the Food and Agriculture Organization of the United Nations: Approximately one-third of all food produced in the world for human consumption every year goes uneaten.

In the first part of the problem, student teams used mathematics to predict whether the food waste in a given state could feed all of the food-insecure people living there. In the second part, teams created a mathematical model that could be used to determine the amount of food waste a household generates in a year based on their traits and habits. They were given four different types of households to consider.

Finally the teams were challenged to make suggestions about how wasted food might be repurposed. They used mathematical modeling to provide insight into which strategies should be adopted to repurpose the maximal amount of food at the minimum cost, and they accounted for the costs and benefits associated with their strategies.

Because such problems are realistic, big, and messy, student teams have plenty of opportunity to make genuine choices about how they want to go about solving them, which mathematical tools they will apply to develop and test their models, and how they will communicate their solution. There’s plenty of work to go around, so all team members can contribute.

If you relate this M3 Challenge modeling problem to the advice from the teacher coaches above, you can see why participation in math modeling competitions as a team sport can help students develop more mathematical confidence, competence, and interest.

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How to Get Better at Math

You get better at math by focusing on understanding—not memorization—while practicing consistently and strengthening your foundation. Most people struggle because they skip basics, rely on shortcuts, or don’t spend enough time solving problems.

This post will teach you how to get better at math faster and with less studying. You’ll still have to study, but it tells you the right things to focus on.

A common issue with most people is that they think math skills are innate. They believe that either you get math or you don’t.

Can Anyone Get Better at Math?

Yes. Math skill is built through practice and understanding—not talent. While some people learn faster, almost anyone can improve significantly by strengthening their foundation and practicing consistently.

In high school, I had this issue as well. I figured that I didn’t get the math gene and ,because of this, there was no chance of me doing anything in my future that required crunching numbers, writing computer programs, or science.

According to psychology, I was a victim of a fixed mindset. I simply didn’t think I could actually get better at math. Or at the very least, I wasn’t willing to sacrifice the time and energy necessary to get my math grade and number skills up.

I was one of those students who actually took pride in my lack of math skills. I avoided challenging myself with more difficult and interesting math and science courses. Beyond what was mandatory, I only took biology so that I could avoid math-heavy physics and chemistry courses

If I couldn’t rely on memorization to get through the class, I didn’t want to study it.

I ordered my high school transcripts to look at my math grades. As you can see, I was not.