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Trouble with Maths? Maths Anxiety? or Dyscalculia?

Rebecca Brown, GDST Trust Consultant Teacher for Maths and WHS Maths teacher, reviews part of Steve Chinn’s paper on The Trouble with Maths – a practical guide to helping learners with numeracy difficulties.

Each learner needs to be understood as an individual and the teaching style and lessons adapted to suit each individual learner.

Is it Dyscalculia or Mathematical learning difficulties? However it may be described, challenges with Maths create anxiety amongst children and adults alike.

The 2017 National Numeracy booklet, ‘A New Approach to Making the UK Numerate’ stated that ‘Government statistics suggest that 49% of the working-age population of England have the numeracy level that we expect of primary school children’. This indicates that having a difficulty with maths should not automatically earn you the label ‘dyscalculic’. So what does it mean to be successful at Maths and why does it make so many people anxious?

Two key factors which aid learning are ability and attitude. Some learners just feel that they can’t do Maths. They feel helpless around Maths. Maths can create anxiety and anxiety does not facilitate learning. Ashcraft et al (1998) have shown that anxiety in Maths can impact on working memory and thus depress performance even more.

More recent research using brain scanning has found that regions in the brain associated with threat and pain are activated in some people on the anticipation of having to do mathematics.

The key question, when faced with a learner who is struggling with learning maths is, ‘Where do I begin? How far back in Maths do I go to start the intervention?’ This may be a difference between the dyscalculic and the dyslexic learner or any learner who is also bad at maths. It may be that the fundamental concepts such as place value were never truly understood, merely articulated.

None of the underlying contributing factors are truly independent. Anxiety, for example, is a consequence of many influences.

Chinn favours the definition of dyscalculia to be ‘a perseverant condition that affects the ability to acquire mathematical skills despite appropriate instruction.’

A learner’s difficulties with Maths may be exacerbated by anxiety, poor working memory, inability to use and understand symbols, and an inflexible learning style. Chinn suggests adjustments to lessons to assist difficulties in maths based on four principles:

  1. Empathetic classroom management
  2. Responsive flexibility
  3. Developmental methods
  4. Effective communication.

In short, the issue is that not every child or adulty who is failing in Mathematics is dyscalculic. Even for those who do gain this label, it does not predict an outcome or even the level of intervention but as Chinn suggests whatever teaching experiences this pupil has had, they may have not been appropriate.

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Coutts, Director of Sport, gives a short review of Make it Stick, The Science of Successful Learning by Brown, Roediger and McDaniel

She considers the ‘illusion of mastery’ and how metacognition can help students avoid falling into this trap with our games players

 

In Make it Stick, P. Brown, H. Roediger III and M. McDaniel discuss the Science of Successful Learning. In general, it’s an incredibly interesting book peppered with examples of how we learn most effectively. Being aware of how we learn and think, can result in an improved ability to problem solve, decision make and over-come hurdles (apologies for the sport pun!). The content is enjoyable, supported by various examples and easy to consume – it’s almost as if they know how to convey information and make it memorable!

This book begins by addressing how learners can fall into the trap of the ‘illusion of mastery’. This is where pupils think they have grasped what they have been taught but once tested fall short. Frequently the revision strategy for this approach would involve making notes and then reading and re-reading them time and time again, simply creating the feeling and appearance of mastery.

With the return of competitive sport on the horizon, I turned my thoughts to how I was going to avoid this illusion with our Wimbledonian games players and make the most of this insight.

Practically in Sport, we must then be careful of striking the balance between enhancing the efficiency and fluency of skills, at the detriment of pupils being able respond flexibly and adapt to an unknown scenario during competition.

When teaching open skills, for example during invasion games eg Netball, adopting a games-sense approach is a desirable method. This allows pupils to become more self-aware, encouraging meta-cognition and evaluation of their own success criteria. It helps them to really judge when they have grasped a skill and perform it under pressure, rather than think that they have without success to prove it. This means that the pupils are improving their skills in a more realistic environment so that they are transferable to high-level competition against other schools. Furthermore, the ability to reflect on your performance and then have a flexible skill set when responding is useful when a taught ‘set play’ is challenged by the opposition. This means that pupils can’t fall into the illusion trap as they are constantly being challenged and having to apply their knowledge and skills appropriately.

Another important aspect of learning in sport is the ability to recognise when similar situations occur during this open environment. In a match context, quick recognition of when a ‘set play’ could be implemented is beneficial as it allows pupils to respond effectively whilst under pressure. It also encourages reflection on your own learning and performance.

Although this games-sense approach needs a good skill base to be effective, I think that it prepares pupils for competitions more effectively by helping them to become better critiques of their own learning than solely focusing on closed drills.

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Jaime-Lee, Head of Netball and Head of Year 10 at WHS, explores the journal article ‘Metacognition and Action’

Jaime-Lee, Head of Netball and Head of Year 10 at WHS, explores the journal article ‘Metacognition and Action’ to consider how to use metacognition to become elite in sport.

MacIntyre, T., Igou, E., Campbell, M., Moran, A. and Matthews, J. (2014). Metacognition and action: a new pathway to understanding social and cognitive aspects of expertise in sport. Frontiers in Psychology

Success in sport has traditionally centred around executing motor skills under competitive conditions. Sport provides benchmarks to distinguish the elite from the amateur, through performance outcomes (e.g. placing in a race), player statistics (e.g. shooting percentage in Basketball) or level of competition (e.g. National vs. County). In addition to the data that is readily available to all performers, athletes are looking beyond the strictly measurable in order to advance in their sporting area.

Metacognitive processes have become a pivotal part of an elite athlete’s repertoire to give them the competitive edge. In sport, metacognitive processes can be used in a variety of ways both in training and in competition. Below are some examples of how athletes can use metacognition to better their physical attributes.

  • The use of mental imagery and mental practice, in which athletes play out physical skills and/or scenarios in their mind. This could include, an athlete imagining themselves in the starting blocks, acknowledging all of their senses.
  • Pre-performance routines, in which an athlete engages systematically in a sequence of actions prior to their performance. This could include, stepping out an athlete’s run up in Long Jump or the position a ball is placed while taking a penalty kick.
  • The use of strategies and set plays, in which decision making is done prior to an athlete’s performance. This could include, anticipating your oppositions movements in Netball and planning counter moves.

The use of metacognitive process not only reduces the chances of error but maximises an athlete’s physical capabilities. Elite athletes need to be not just be experts in movement execution but also experts in controlling their own mental processes.

 

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John Gunn, Teacher of Religious Studies at WHS, emphasises the importance of “being careful to think about thinking” as teachers

Have you ever walked into a classroom and made an initial judgment which you can’t see to amend? Perhaps when we make initial observations, we are comparing two things and judging their similarities? If our judgments are distorted by perception, how can we be sure that our decision making is having a positive impact on teaching and learning? This is why it is so important for us to think first about why we think the way we do. Not only will this reflection allow us to consider how we come to make judgments, but also make us factor in the unknown in our decision making.

 

The Undoing Project – Michael Lewis

On each round of a game, 20 marbles are distributed at random among five children: Alan, Ben, Carl, Dan, and Ed. Consider the following distribution:

Type I   Type II  
Alan 4 Alan 4
Ben 4 Ben 4
Carl 5 Carl 4
Dan 4 Dan 4
Ed 3 Ed 4

 

In many rounds of the game, will there be more results of type I or type II?[1]

If you have spent a moment looking at the above example, I wonder if you thought why you chose type I or type II. What are we doing when we make judgments? How do we take pieces of information, process them, and come to a decision or judgment?

For one or more answers, I recently read The Undoing Project by Michael Lewis in which he tracks the careers and lives of two of the greatest psychologists, Danny Kahneman and Amos Tversky.

The above table is taken from Lewis’ book, chapter 6, The Mind’s Rules. Questions such as, ‘when/where was human judgment likely to go wrong’, ‘why do people often say that they were doing one thing when they were actually doing another’ ‘what are people doing when they judge probability’ are examples which Kahneman & Tversky try and tackle. In their paper Subjective Probability: A Judgment of Representativeness[2] Kahneman & Tversky attempt to ‘demonstrate people make predictable and systematic errors in the evaluation of uncertain events’. If nothing else this should get you thinking about thinking. Part of their approach comes from the premise that when people make judgments, they compare whatever they are judging to some model in their minds. “Our thesis is that, in many situations, an event A is judged to be more probable than an event B whenever A appears more representative than B.”[3] So, take a look again at the above example. Do you know why you chose type I or type II? If you think that the uneven distribution of type I is more likely than all the children receiving four marbles each, then think again. Just because type II “appears too lawful to be the result of a random process…”[4] it doesn’t mean it is wrong. This is something worth thinking about, “if our minds can be misled by our false stereotype of something as measurable as randomness, how much might they be misled by other, vaguer stereotypes?”[5]

Throughout the book there are questions raised about our understanding of how hard it is to know anything for sure. Kahneman himself favoured Gestalt psychology which sought to explore the mysteries of the human mind. The central question posed by Gestalt psychologists was, ‘how does the brain create meaning?’ Look at the two parallel lines below.[6] Are you really going to insist that one line is longer than the other?


If perception has the power to overwhelm reality in such a simple case, how much power might it have in a more complicated one?

For those of you of a more medical persuasion you may prefer Chapter 8 which tracks the impact Kahneman & Tversky had on Dr. Don Redelmeier, an internist-researcher. Working at Sunnybrook, Canada’s largest trauma centre he says, “You need to be so careful when there is one simple diagnosis that instantly pops into your mind that beautifully explains everything all at once. That’s when you need to stop and check your thinking.”[7] This is not to say that the first thing that comes into our mind is wrong, but because it was in our mind, we become more certain of it. How costly may this be in school life? This I think is highlighted in an example of a maths problems in which we can check our answers to see if we have erred. In comparison to education it highlights an interesting thought. “…If we are fallible in algebra, where the answers are clear, how much more fallible must we be in a world where the answers are much less clear?”[8] This is certainly a book to read from cover to cover even if it doesn’t give you all the answers why we should be careful to think about thinking.

[1] Lewis, P176

[2] Published 1972

[3] Lewis, P182

[4] Subjective Probability: A Judgment of Representativeness, p5

[5] Lewis, P184

[6] Lewis, P76

[7] Lewis, P214

[8] Lewis, P221

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George Cook, explores ideas from The Culture Code (Daniel Coyle) and Radical Candor (Kim Scott)

George Cook, Head of Hockey at WHS, explores ideas from The Culture Code (Daniel Coyle) and Radical Candor (Kim Scott). These books show that it is less about the questions we ask, and more about the environment we create that enables us to ask them. Culture is everything.

Questioning is a hot topic in the world of education. What type of questioning do you use? What type of questioning should you be using?

There is no doubt that questioning allows us, as the teacher, to identify areas of strength and weakness in our classes. It gives opportunity to really challenge the most gifted, stretching and pushing the limits of their understanding. It is a great tool because in the same breath we can use questioning to give great confidence to those who are unsure or perhaps, normally, quieter and more reserved in lessons.

However, according to the two books listed above, the type of question you use and who you ask it to, is irrelevant if the environment we create is not quite right.

The Culture Code examines many high performing groups ranging from high end military task forces and airline pilots, to successful start-up companies as well as big hitters like Google. On the face of it, none of these groups have much in common. Apart from the culture they have developed, built on honest two-way communication and trust.

It was found that regular small snippets of communication within these high functioning groups allowed them to not only know each other better, but made sure they stayed on track throughout the task at hand to complete it in the most accurate and efficient way possible. The opposite of this in a classroom situation would be to wait for over an hour into a lesson before catching a pupil off guard with a challenging question to answer in front of their peers. Small and frequent two-way communication is much more effective.

Radical Candor states that if we are to have open and honest communication in our groups and teams then we must instil two key elements first. Firstly, care personally about all those in your class, and show it! As teachers we do this more often than we might expect and can be as simple as asking a pupil how their weekend was etc. The second element is to challenge directly. Challenge the beliefs of pupils directly, but also actively encourage them to do the same to us as this is more likely to build trusting relationships where more in depth and honest discussions and conversations can be had.

If we can take these lessons and implement them into our classroom and practical teaching, then we are far more likely to have open and lively debate and discussion that includes all members of the group and not just those that feel confident in the subject area. This is why I think the culture we build around questioning is equally important as the type of questions we use.

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Steph Harel, explores the journal article ‘Developing enquiry through questioning’

Steph Harel, Acting Head of Geography at WHS, explores the journal article ‘Developing enquiry through questioning’

Wood, P. (2006) Developing enquiry through questioning. Teaching Geography, 31(2), 76-78.

“Any student wising to develop their capacity to enquire geographically requires a clear capacity to question” (Wood, 2006; p. 78).

Many classrooms, and even national strategies, focus on teachers as the main questioners; however, if students are to develop an independence in their work they must gain experiences which allow an opportunity to play a central role in framing questions of interest.

Wood accurately argues that students need to develop their questioning skills if they are to act as autonomous enquirers. His valuable exploration into different ‘levels’ of questioning in Geography highlights meaningful ways in which to support students to develop their own capacity for independent questioning:

1. Simple questioning: Simple questioning games can be used to develop and sharpen students’ questioning skills. For example, when revising a physical geography topic, students are given a post-it note with a keyword written on it, which they stick to their foreheads. Students then pose each other ‘yes’ ‘no’ questions to decipher which process they have been allocated.

2. Questions to compare: Students are asked to develop questions which will produce a clear and detailed comparison. For example, students studying tectonic hazards might explore two case studies, one from an AC and one from an LIDC, and are asked to compare their volcanic eruptions by posing questions. Importantly, students then reflect on why they have chosen their questions.

3. Questions to enquire: Wood uses an example of a KS3 class, who recently completed a unit on agriculture. Students were prompted to consider the underlying patterns and processes they studied and asked to formulate five questions they would use to investigate the agriculture of India. For example, “How does landscape and climate affect farming in India”? I was particularly struck by Wood’s focus on the importance of recognising that enquiry questions can lead to ‘dead-end’ responses, and that learning and understanding is not a simple or linear process.

4. Questions to research: When students have developed a questioning capability, they can be given a large amount of autonomy in both framing and researching questions. Wood explores this idea in KS5 Geography teaching, with students studying the global economy. Students were offered a new context in which to explore the changing economic fortunes of two contrasting locations and the opportunity to decide on questions they felt were pertinent to ask. The process culminated in a written report, which demonstrated deep and critical understanding of the information researched.

As an educator, it is my belief that the geography classroom is an ideal environment for developing the use of self-questioning. I found huge value in Wood’s article, which argues that it is crucial that teachers not only learn how to pose their own questions to greatest effect, but also guide and support students in developing their own enquiries about the world around them. “By focusing on the student as questioner, we can help them become more active, reflective learners, and this can only help in developing active, critical classrooms where quality geography [my emphasis] can blossom” (Wood, 2006; p. 78).

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Alexa Cutteridge reviews ‘The Coaching Habit Say Less, Ask more & Change the Way you Lead Forever’

Alexa Cutteridge, Head of Curriculum PE and Assistant Head of Year 7, gives a short review of ‘The Coaching Habit Say Less, Ask more & Change the Way you Lead Forever’ by Michael Bungay Stanier

 

“We live in the world our questions create.” (David Cooperrider)

“The minute we begin to think we have all the answers, we forget the questions.” (Madeleine L’Engle)

“Get comfortable with silence”

“Without a good question, a good answer has no place to go” (Clayton, Christensen)

–

As a PE teacher, I have spent most of my professional career practically coaching on the sports field, but I have been on a journey to bring coaching techniques to my leadership roles, and apparently, I am not alone! As noted in the book, Daniel Goleman (psychologist and journalist who popularised the concept of emotional intelligence) suggested that coaching is one of the six essential leadership styles, but is one of the least used as many leaders claim to not have time to practise it. Stanier guides you through easy ways to change your leadership behaviour, to incorporate a coaching style in a way that you do ‘a little more asking people questions and a little less telling people what to do.’ Stanier considers that it is not initially an easy concept to increase questioning and so he helpfully outlines how to change, before looking at what to change.

The seven coaching habit questions are:

  • The Kickstarter Question – ‘What’s on your mind?’ the way to start any conversation in a way that is both focused and open.
  • The Awe Question – the best coaching question in the world – ‘And what else?’ This works as a self-management tool for you, and as a boost for the 6 other questions.
  • The Focus Question – ‘What is the real challenge for you here?’ This question helps you slow down so you can solve real problems and not just the first problem.
  • The Foundation Question – ‘What do you want?’ This allows you to identify the needs of an individual and get a better understanding how you can support them.
  • The Lazy Question – ‘How can I help?’ This helps cut right to the request and additionally it stops you from leaping into action unnecessarily.
  • The Strategic Question – ‘If you’re saying yes to this, what are you saying no to?’ This allows the people you are working with to be fully committed to their yes and aware of the no’s which will create the space and energy for the yes to happen.
  • The Learning Question – ‘What was most useful for you?’ This works with the Kickstarter question to make the Coaching Bookends. It helps to ensure that everyone finds their interactions with you even more helpful.In the educational arena, applying the coaching habit and the simple, yet powerful seven questions, has the potential to positively transform the leadership of Teachers, Heads of Departments, Pastoral Leaders, Senior Management or even pupils on Student Leadership Team. After reading this book, it is important to highlight that I do not think we need to do away with the leaderships styles we already have, but merely bring the coaching habit questions into the mix, in a way that works for us. How does that sound?
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Jamie-Lee explores the Journal of Health, Sport and Physical Education

Jaime-Lee, Head of Netball at WHS, explores the journal article ‘Questioning for Learning in game-based approaches to teaching and coaching’ from the Asia-Pacific Journal of Health, Sport and Physical Education

 

Harvey, S. and Light, R. (2015). Questioning for Learning in game-based approaches to teaching and coaching. Asia-Pacific Journal of Health, Sport and Physical Education, 6 (1): 1-16.

‘Questions that encourage players to reflect on what they have just done will increase learning’.

A Games-based approach is just one pedagogy used in the teaching of PE. It is focused around practice through play, where players learn and refine skills while participating in matches. As skills are not broken down and taught individually, questioning becomes an important part of the learning. In order to achieve a Games-based approach, the PE teacher needs to move away from the traditional direct instruction teaching to open-ended questioning within the game of play.

The Games-based approach draws on 2 theories of learning – ‘The Zone of Proximal Development’ and ‘Complex Learning Theory’. The Zone of Proximal Development looks at focusing questions in the gap between what a player can learn on their own and what they can learn with direct teacher guidance. Complex Learning Theory focuses on the idea that learning is a combination of the mind and body.

Examples of good questioning in a Games-based approach:

  • How are you deciding when it is best to lead for the ball?
  • How could you improve your off-the-ball defence?
  • What is the most important thing to think about when deciding who to pass to?
  • What might happen if you do not receive the ball on your first drive?

Questioning needs to be open and give the player the opportunity to reflect on what they have just done. For players to show skill progression, they need to understand why they were successful/unsuccessful and how they can improve. For example, if a player is struggling to get free on a centre pass, rather than saying, ‘if you dodge it will help you get free’. Try, ‘how can you get free from your opponent?’, followed by ‘what if that does not work?’.

When done well, a Games-based approach allows players to not only make decisions independently but also to adapt to new or changing situations as they arrive. The use of well-constructed targeted questions will increase a player’s knowledge beyond where they could have reached on their own. The key is to ask open-ended questions at a point in play where reflection can occur.

 

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Mr Richard Bristow explores an article from Music Teacher Magazine

Music Teacher Magazine

Mr Richard Bristow, Director of Music and SMT Secondee, explores an article from Music Teacher Magazine looking at the idea of establishing ‘desirable difficulties’ in the way we use questions and approach tough concepts.

‘For music teachers, there are four overarching strategies that are most useful for introducing desirable difficulties into a music education context – recall practice, interleaving, the spacing effect and elaborate & listen’.

Passey’s impressive article quickly discusses some very useful strategies that musicians, working in the classroom, practice room or (eventually!) on the stage, can employ to help our learners overcome struggles and difficulties in our lessons. At the heart of this is often the ‘teacher as expert’ message which can be problematic to our learners, as they can so often see how effortless we, as professional musicians, can make something, whilst they are struggling with achieving the same technique. So much of this is linked to the way we present information. As Passey argues, it is far better for long-term memory to engage learners by active questioning and quizzes than to simply give them the information, where up to 50% of the information gets lost in future recall.

The recall strategy is something musicians use frequently; whether this is leaning specific exercises like scales or learning entire pieces from memory, as many of our scholars and performers at the WHS Young Musician events do. The huge benefit, as Passey summerises, is that finding learning something from memory difficult helps to reinforce the strength of the memory, ensuring the memory remains active and accessible in the future. The questions we ask are central to this; the learner might find playing from the score easier initially, but needs to be encouraged, through questioning, to see the development of their musical skill as being the ultimate goal. 


The discussion on interleaving was also great to read, building on work we as staff have been doing on this in WHS recently, but with the benefit of close subject-specific focus. This involves switching between many different by related tasks, forcing the brain to make links with multiple pathways (‘desired difficulty’) rather than learning something in a ‘massed practice’ way, where the same bar or passage gets repeated over and over, forming a single pathway. I really like the idea of having interleaved practice sessions, where learners switch between playing pieces, exercises and aural skills to see the links between them and develop musical skills. Perhaps switching between instruments would provide even more connection, and I’m now wondering if asking my choir to perform their parts on instruments could really aid their musicianship. Again, the questions we ask form the backbone of creating links and avoiding potential cognitive overload and confusion.

The spacing effect is also another area where musical skill can benefit other subject learning. Long term recall is hugely helped by doing smaller amounts of practice regularly rather than lots of practice once a week. The same is surely true of exercise, and, as we head into Lockdown 2 at the time of writing, is something I am going to try to do more of!

The final passage, titled elaborate & listen, was for me the area that will have the most impact on my teaching, whether in the classroom or on Teams. I really enjoyed the idea of transformative improvisation – where you take an idea and improvise around it – as this is something that is useful to the performer, composer, and musicologist. Extending this by altering the style we perform in (‘try learning this passage of Mozart, but playing it in a Ragtime style’) can also be useful to develop these neurological pathways, and again something that readily transfers from practical performance to composition and the written word. The idea of listening is also vital; when we ask a question, how often do we actually listen to the answer? Sometimes the best question is one that gives the learner space to talk about their experience, vocalising the connections they are perhaps starting to make.

Regardless of the subjects we teach, and how we teach them, the idea of ‘desirable difficulty’ is an excellent one that comes from the questions we ask in our contexts. Celebrating challenge by asking difficult questions and enjoying the journey of learners answering with increased fluency is something to be relished.

 

Article title: An upward curve
Author: Guy Passey
Featured in: Music Teacher Magazine, October 2020 (accessed through the paper mag, not online)

 

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Mrs Rebecca Brown reviews Craig Barton’s book: How I wish I’d taught Maths

Mrs Rebecca Brown, teacher of Maths at WHS, reviews Craig Barton’s book How I wish I’d taught Maths, focusing on Chapter 11 about formative assessment and diagnostic questions.

“without an effective formative assessment strategy we are in danger of teaching blindly, being completely unresponsive to the needs of our students.”

Craig begins this chapter by referencing the 2013 Dylan Wiliam tweet:

Example of a really big mistake: calling formative assessments ‘formative assessment’, rather than something like responsive teaching.

It’s only a too familiar scenario – you mention an assessment and a classroom (or staffroom!) erupts into a panic of more pressure and visions of tests, marking and grades. But how do we understand what our pupils know and where we need to begin or continue teaching them from? Even more crucial now, following a period of prolonged guided home learning. My key quotation from the chapter is when Craig explains that ‘without an effective formative assessment strategy we are in danger of teaching blindly, being completely unresponsive to the needs of our students’.

Formative assessment should be about ‘gathering as much accurate information about students’ understanding as possible in the most efficient way possible and making decisions based on that’. In short, it is about adapting our teaching to meet the needs of our students.

He describes elements of great teaching and cites one of Rosenshine’s (2012) ‘Principles of Instruction’ -to check for student understanding: ‘The more effective teachers frequently checked to see if students were learning the new material. These checks provided some of the processing needed to move new learning into long-term memory. These checks also let teachers know if students were developing misconceptions’.

Teaching is only successful if students have understood and learned something. Successful formative assessment can help us to identify problems and begin to fix things in the here and now much more effectively and efficiently. Asking ourselves, do I need to go over this point one more time or can I move on to the next thing?

Craig suggests the use of diagnostic questions to give quick accurate and useful information about students’ understanding. A good diagnostic question is a multiple choice, four-part question, with three incorrect answers that can help you to identify both mistakes and misconceptions. Each incorrect answer must reveal a specific mistake or misconception. If the question is designed well enough, then you should be able to gain reliable evidence about students’ understanding without having to have further discussions.

Diagnostic questions are designed to help identify, and crucially understand students’ mistakes and misconceptions in an efficient and accurate manner. They can be used at any time in a learning episode and are most effective when used throughout, using follow up questions to test the exact same skill as the first question.

Craig has developed a website of diagnostic questions that can be used in a variety of subjects. This year I will be trying to incorporate these into all of my lessons to ensure I have accurate, timely information on student understanding to enable me to effectively teach the girls that I have before me.