What effect has this investigation had on me personally?

The million dollar question. When I began this investigation, I identified that I hoped the process was going to be somewhat cathartic. And, to some degree it has. Being forced to confront the psychological and emotional component of mathematics theory certainly engenders critical reflections of ones own deep seated beliefs.

 I realise that we as parents had a part to play in my son's development of maths anxiety through overly high expectations. However, it was a combination of factors that made him susceptible to developing maths anxiety. It is easy for me to accept that maths anxiety has neurodevelopmental origins; emotional self-regulation is an issue my son struggled with when younger (and to a lesser degree he still does). This coupled with low mathematical self-concept and poor performance in the early years  of school meant that it was almost inevitable that he develop maths anxiety. I say almost because it is equally obvious that maths anxiety can be reduced in the classroom by sound practice. In the early years of my son's schooling, there was a heavy reliance on teaching "number sense" to the exclusion of all else, and as a consequence he never developed a solid foundation of basic facts that he could retrieve with any level of automaticity. 

From my journey, it is clear through the research that teachers are the prime determinant in the development of maths anxiety. I believe I am now more readily able to identify the risk factors that contribute to maths anxiety and how they might play out in the classroom. Moreover, as a teacher, I am congnisant of the fact that I have the ability to mitigate the effects of maths anxiety and even reduce the likelihood of it occurring in the first place. The starting point is my attitude, and all else follows from there. Our mathematical programmes must be designed to meet the needs of every individual learner in the classroom. However, this is said with some sense of trepidation, hoping that in a National Standards driven system mathematical programmes do not become constrained by the very mechanism that was supposedly designed to enhance learning. Maths anxiety prevalence could conceivably increase from the estimated 25% of students it now sits at. Bearing this in mind, it is even more important that teachers are aware of the debilitating affect of maths anxiety, and equally, teachers must be strong advocates for a more just and fair anxiety free maths curriculum.

.

Teaching that counteracts Maths Anxiety

Yaratan & Kasapoglu (2012) make the following statement, which to me seems synonymous with all we have been taught on our journey so far as pre-service teachers. Moreover, the approach they advocate is, I feel, congruous with the intent of the New Zealand Currcilumum:

In their teaching, teachers should always concentrate on the comprehension of the main concepts, use of mathematical terminology correctly, communicating mathematically, developing problem solving skills, transferring mathematical knowledge to real life situations, but above all, teachers should design leaning activities which would be appropriate to the ability of each individual student in their classes. Student-centered teaching methods, creative activities such as group work, mathematics projects and mathematical games should be employed by teachers to make their students enjoy mathematics.

                                                        Yaratan & Kasapoglu (2012, p. 169, emphasis added)

To use an often quoted mantra, “It’s not rocket science…” Student-centred teaching underpinned by formative practice to meet the needs of each and every learner in the classroom is not a new or controversial epistemological argument. However, this may be an overly simplistic and idealistic view. If there was a simple solution then surely maths anxiety would obviously not be the major issue it undoubtedly is (If potentially 25% of my students may exhibit some degree of maths anxiety, it is unequivocally a major issue for me and them!).

I believe the first step is ensuring that as a teacher you are not a perpetuator of maths anxiety. Your attitude towards maths, where you may be the only ‘mathematician’ students have contact with, is perhaps one of the most cogently influential –and controllable- factors in the classroom. There needs to be a balance in your maths programme. I was struck by the tension apparent in the competing arguments around rote/repetition and number sense. Students at risk of maths anxiety need to be able to be able to retrieve information (such as basic facts) to free up working memory, and similarly they need to have number sense to help alleviate anxiety.  I think educationalists in the past have been guilty of pushing the ‘theory du jour’ to the exclusion of all else…students need to develop both number sense and a store of retrievable facts.

There are, however, practical strategies that can be used to lessen the affects of anxiety. Sheffield and Hunt (2006) identify “two types of intervention strategy: behavioural approaches that focus directly on the emotional component of maths anxiety, and cognitive approaches that focus on altering the negative thought’s (e.g., “I’m useless at maths”) contributing to anxiety” (p. 22). They believe that the most effective interventions are behavioural interventions, as opposed to those that target cognitive or intellectual abilities. One approach they reported success with involved instructing children in the practice of “relaxing diaphragmatic breathing, using imagery to reduce anxiety, and in situ desensitization” (p. 22). The in situ desensitisation relate to the gradual exposure to problems of increasing difficulty while practicing relaxing breathing. One final point they make is a recommendation for teachers to actively mitigate ‘threatening’ situations such as assessments. High stakes assessments and time constraints have already been discussed as injurious causes of maths anxiety.

This last statement has real implications for us and the National Standards discourse. National Standards has the potential to cause students with maths anxiety, who may be below the standard, to spiral downwards even further. Similarly, why is assessment so determined by the element of manageability through time constraints? Time constraints undermine the validity (fairness) and reliability of assessments, and we as teachers need to consider this for each and every task in the classroom. So, my journey is nearly at an end…perhaps, all that remains is for me to quietly ruminate on what I have learnt and discuss the body of work in relation to the implications for me personally.

Teaching Maths Anxiety

As already implied, teachers play a significant role in the maths anxiety discourse. Firstly, like parents, a teacher’s attitude towards mathematics is extremely influential upon the students within the classroom. Teachers, through a subtle form of osmosis, may unconsciously, through class interaction and dialogue, pass on to students their own attitudes and anxiety towards mathematics (Stolpa, 2004, p. 4). Interstingly in a study of college majors by Hembree (1990, in Ashcraft & Krause, 2007, 9. 247) it was identified that those subjects who tested highest for maths anxiety were those preparing to become elementary school teachers!

In my first year of study as a pre-service teacher, when completing an introduction to numeracy paper, a number of my fellow students struggled. They constantly expressed their dislike of math and their inability to understand concepts, and knowing what I know now, I would suggest some exhibited high levels of maths anxiety.

According to Ashcraft & Krause, the result of this is that students in primary school are in danger of being ‘stranded’ in classrooms where the teacher may ‘possibly defensively adopt a cold, unsupportive approach’ (p. 247). Sheila Ford, a former teacher, principal and member of the US board for the National Assessment of Educational Progress, contends that “student uneasiness in maths tends to rise faster if they have a sense that a teacher does not have mastery of the material” (Cavanagh, 2007, p. 12). I strongly believe it is incumbent upon us, as prospective teachers of mathematics, to ensure that we are prepared and have the required pedagogical content knowledge to successfully meet the needs of all learners (mathematicians) in our classrooms.

Curriculum and Pedagogy

Curriculum and pedagogy both bear consideration, too. As alluded to earlier, a wide body of research suggests maths anxiety only really begins to manifest in primary school. Geist (2010) and others highlights the detrimental effect formal schooling can have. Children who have previously constructed mathematical conceptual understanding are confronted with textbooks, teacher imposed solutions and methods, repetition, and an over reliance on high stakes timed testing. High stakes timed testing and repetition are especially insidious for students at risk of maths anxiety; they invariably use more working memory for these tasks and as such “choke under the pressure” (Cavanagh, 2007, p. 12). Similarly, anxiety can be aroused when students are directed to solve problems on the board or in front of the class, subject to performance pressures (progress charts, tests), and when they are exposed to new concepts without developing the framework to support the new learning (Geist; Ashcraft & Moore).

However, teachers can make a positive difference for students who have Math anxiety. Some simple suggestions will be discussed next. 

And, it is worth noting that the majority of these suggestions should really be just a matter of good practice for all students…

Parental expectations and maths anxiety

In an unsurprising statement, Yaratan & Kasapoglu (2012) contend that "parents play an important role in shaping their children's attitudes and anxiety," as children inevitably imitate the attitudes and behavior of their parents (p. 169 emphasis added). Likewise Stolpa (2004), when discussing writing and maths anxiety, reminds us that children are not born believing they are incapable of achieving success; lack of self-efficacy is learned from the world outside where parental attitudes and expectations are a [some would argue the] key contributing factor (p. 3). Of note, is that Geist (2010) posits that these negative attitudes towards maths begins early in life prior to starting school, and moreover, much of the mathematical foundational conceptual development occurs in the first months and years of life through interaction with adults and the environment (p. 24).

But this is where the argument around parental expectations gets blurred. Overly high expectations are just as likely to contribute to maths anxiety as inordinately low ones, and again the 'chicken and egg causality' features prominently in the literature. A child who is unable to meet parental expectations experiences a loss of self-efficacy which is compounded by (sometimes perceived) negative feedback from parents with high expectations. Whats more, Ashcraft & Moore (2009) suggest that some children are more self-focused, and thus vulnerable to anxiety whereby they internalise negative feedback from poor performance leading to anxiety (p. 247).

This scenario is symptomatic of my own experiences. My son, in his struggles with maths, was assessed by a RTLB who clearly identified that he was more self-focused (egocentric) and struggled with affective control. 

As already mentioned, parents who themselves struggled with mathematics are likely to unintentionally transfer or transplant those attitudes onto their children. Further, parents being parents are often want to shield or comfort their children. So, when their child is struggling, parents confirm a student's sense of futility by suggesting they shouldn't worry as they had the very same issues "Don't worry...maths was never my strong suit, too" (Geist, 2010, p. 3). Students pick up this mantra and develop a belief that they are genetically deficient in maths ability (ibid., p. 3)which leads to global avoidance behaviours (Ashcraft & Moore, 2009, p .247). 

What can we as parents do?

Obviously, as parents we need to understand the vital role we play in shaping our children's attitudes towards maths. Yaratan & Kasapoglu suggest we need to talk about maths in a positive manner and have realistic expectations. We should help our children with maths where possible, and encourage them to seek extra help as required. Further, they highlight that it is important that we understand that forcing children to do mathematics against their will, when they are struggling with anxiety or efficacy, is counterproductive (p. 169). Ashcraft & Moore (2009, p. 203) also highlight research that indicates children who have poor "number sense" are more likely to perform poorly and develop anxiety which relates to Geist's argument about the importance of developing mathematical concepts early in life. Parents need to expose their children to mathematical language, concepts, and thinking through everyday conversations and games during early childhood. Hunt & Sheffield (2006) present specific anxiety related interventions which are applicable for both home and school. These will be discussed in more detail in my next posting.

What I take from this passage of research, is that parents are critically responsible for the attitudes a child develops towards mathematics, and they contribute to the conceptual foundation that a child brings to the classroom. However, the literature tends to suggest that maths anxiety only really begins to present in the classroom. In fact Geist (2010) cites Jackson & Leffingwell (1999) who state that "teacher behavior was a prime determinant of math anxiety and that it is usually evident early on in the primary grades" (p. 28).

Yaratan, H. & Kasapoglu, L. (2012). Eight grade students' attitude, anxiety, and achievement pertaining to mathematics lessons. Procedia - Social and Behavioral Sciences 46, pp. 162-171. Retrieved (with thanks Merilyn) from:

http://www.sciencedirect.com/science/article/pii/S1877042812012165

Recognising Maths Anxiety

Sheffield & Hunt (2007) suggest that studies on the prevalence of maths anxiety with students in the USA indicate that 25.9% of students had moderate to high needs with maths anxiety (p. 19). While  there appears to be little or no data from a New Zealand perspective, it would be reasonable to assume that up to a quarter of students in our classrooms could be detrimentally affected, to some degree, by maths anxiety. So, just how is maths anxiety diagnosed? 

While there are also the obvious physiological manifestations discussed in earlier postings (flight or fight) which are both measurable and observable (see the cartoon above!), the literature suggests that the predominant method of diagnosis to determine maths anxiety is by using the Maths Anxiety Rating Scale (MARS). The MARS is a lengthy self-report questionnaire which asks respondents to rate their level of anxiety when responding to maths-specifics situations (ibid. p. 19). Further, there are various lengths and versions of the MARS available to cater for the different needs and age appropriateness of students (Ashcraft & Moore, 2009). 

Of late, there is also an increasing body of research investigating the neurodevelopmental origins of maths anxiety. In a study (heavy reading) by Young, Wu, & Menon (2012) that incorporated neuropsychological assessments and functional brain imaging using MRI, they posit that maths anxiety is "associated with aberrant activity in the right amygdala" portion of the brain. Whats more, they highlight that this is consistent with research that links the amygdala with the regulation of cognitive-emotional behaviours (p. 499).

This is all well and good, but what do I, as a classroom teacher, need to know from a lay perspective of maths anxiety? Firstly, in a somewhat surprising finding for me, the literature all tended to suggest that maths anxiety on the whole was more of an issue for girls than boys! It is generally accepted that boys and girls brains function differently (no kidding!!), and Geist (2010) points out that many classrooms still operate on a traditional  'skills based' model of instruction which is incompatible with how many girls learn. Further, it is likely that girls are less adaptable and particularly struggle with high stakes testings and time constraints, and that parental and teacher expectations (societal) of girls not being good at maths become self-fulfilling (p. 25). 

Interestingly, this type of issue arose at my base school last year where female students were competing against each other to gain entry into a local prestigious all girls schools. One student in particular became noticeably anxious with her physical and emotional well-being deteriorating to the point where she had to receive counselling...she was only 10 years old :-( 

Especially relevant, is the fact that poverty also shapes as a consistent indicator of  poor maths performance and maths anxiety. This can be generally explained by low levels of parental expectations, mathematical efficacy, and educational attainment which in turn shape the child's own beliefs (p. 28). 

Parental and teacher expectations (and instruction) are close to the heart of my journey, and I will explore these is terms of maths anxiety in my next posting.

Geist, E. (2010). The anti-anxiety curriculum: Combating maths anxiety in the classroom. Journal of Instructional Pschcology; Mar 2010; 37, 1. Retrieved from:

http://go.galegroup.com.ezproxy.waikato.ac.nz/ps/i.do?action=interpret&id=GALE%7CA224405375&v=2.1&u=waikato&it=r&p=AONE&sw=w&authCount=1

Young, C., Wu, S. & Menon, V. (2012). The neurodevelopmental basis of maths anxiety. Association for Psychological Science. Retrieved from:

http://pss.sagepub.com/content/23/5/492

Working memory...what is it, and how does it effect maths anxiety (or vice versa)? 

As alluded to in my last post, working memory is and integral component in math performance or ability. Ashcraft & Krause (2007) reiterate this point to suggests mathematical cognition is reliant upon working memory, and further, they refer to research to state that there is a positive relationship upon the demands of working memory when solving more complex arithmetical problems (p. 243). But, just what is working memory?

For the more mature mathematician, working memory is another name for short-term memory. Sweller et al. (1998) describes it as "the conscious part of our information processing system; it is where the deliberate thinking takes place" (Eggen & Kauchak, 2004, p. 240). Sweller points out that we "are probably only able to deal with two or three items of information simultaneously when require to process information rather than merely hold information" which has obvious implications for problem solving. Further, Ashcraft & Krause (2007 citing a wide body of literature) suggest this heightened draw upon working memory has been exacerbated by an increasing tendency to solve larger operand problems using non-retrieval processes such as counting, reconstruction, or other strategies. Further, it has been proven that non-retrieval processing is invariably slower and more error prone that memory based retrieval (p. 244).

This seems particularly pertinent. With 'number sense' coming to the fore, I believe there was  a conscious diminishing of 'rote' learning-teaching in the classroom. Consequently, a number of students (my son included) never developed mastery of their basic facts even at a limited level. Hence, when trying to solve problems they don't have instant recall to call upon and have to work twice hard to process and solve problems. Interestingly, on placement this year at intermediate level, they had noticed similar widespread issues and were initiating a real push on basic facts (and algorithms). 

My previous discussion suggested that the affective nature of maths anxiety 'wastes' working memory as students attend to their anxiety, a view supported by Ashcraft & Krause. Therefore, they suggest, it makes sense that as the difficulty of the task increases the available working memory decreases. Moreover, I believe that increased difficulty would heighten anxiety, decreasing even further (an exponential relationship) available working memory for processing tasks.

So, it would appear that working memory is a pervasive presence or requirement for mathematical processing and that it can be severely conflicted by maths anxiety. Thus it seems logical, that as a teacher I will need to be able to identify maths anxiety in my students and perhaps recognise any factors that may significantly increase the risk of a students 'suffering' from maths anxiety. This is my next step...

References

Ashcraft, M., & Krause, J. (2007). Working memory, math performance, and math anxiety. Psychometric Bulletin & review (pre-2011); Apr 2007; 14, 2. Retrieved from:
http://www.andrews.edu/sed/gpc/resources/faculty-research/montagano-research/working_memory_math.pdf  

Eggen, P., & Kauchak, D. (2004). Educational psychology: Windows on classrooms. New Jersey, USA: Pearson Education

The chicken or the egg causality dilemma 

Since my last posting, this thought has preoccupied my thinking around maths anxiety. Does low maths ability (and a resultant low self-concept) lead to maths anxiety, or does the affective state of maths anxiety lead to poor maths performance? As a prospective teacher, getting to the crux of this issue could have important implications for my practice.  

If I return to the Krizinger et al. (2009) article Maths Anxiety and Math Ability in Early Primary School Years, they suggest that a definitive position is far from certain. Citing a wide body of research grounded in behaviourism, they posit that "anxiety emerges as an obligatory response to aversive stimulus" (p. 207). Therefore, they suggest, poor performance or a failure to develop understanding will inevitably lead to negative emotions and maths anxiety. Of note also, is the contention that cultural influences and parental expectations of success may contribute this feeling of underwhelming efficacy.  For me, this resonates with the recount of my son's maths anxiety.

However, the second position presented resonates just as strongly (and perhaps soothes my conscience somewhat). Krizinger et al. (2009) present a school of thought that contends that emotional factors influence cognitive ability.  Avoidance  behaviours that are part in parcel with maths anxiety can increase the disparity in calculation performance which is characterised by a "vicious cycle" where less practice leads to comparatively poorer performances which in turn exacerbates anxiety... Another common symptom of maths anxiety is the manifestation of "worrisome thoughts" which have the ability to absorb working memory. Krizinger et al. (2009) refer to Eyseneck & Calvo's (1992) processing efficiency theory which "states that experiencing anxiety will draw on working memory capacities and therefore will compromise cognitive performance" (p. 207).

The relationship between maths anxiety, working memory,  and maths ability looms large in the literature I have sourced for this project and this is an avenue I want to pursue in my next posting.

Krinzinger, H., Kaufmann, L., & Willmes, K. (2009). Math anxiety and math ability in early primary school years. Journal of Psychoeducational Assessment, 27(3), pp. 206 – 225. Retrieved from:http://jpa.sagepub.com/content/27/3/206 

What is 'maths anxiety' ?

So what is meant by ‘maths anxiety’?

It appears that Richardson & Suinn’s (1972) definition is generally accepted as a broad measure of what constitutes maths anxiety where it is described as a person’s negative affective reaction to situations involving numbers, math, and mathematics calculations, “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations” (p. 551 in Ashcraft & Moore, 2009, p. 197). Ashcroft and Faust (1994, in Sheffield and Hunt, 2007, p.19) describe it in even stronger terms to suggest maths anxiety is “feelings of tension, apprehension, or even dread…” Students may feel their heart beating quicker and demonstrate a lack of self concept towards mathematical problems (p. 19).

This palpable sense of dread was clearly evident in my son as a youngster when faced with mathematics. The emotive or affective aspect seems to resonate strongly within these definitions which somewhat supports a functionalist approach to emotion where emotion is central to all our endeavors including cognitive processing (Berk, 2009, p. 400).Within this construct of emotion-cognition relationship, anxiety directly impacts upon performance with high levels severely impairing performance (p. 400).

Is maths anxiety a specific learning disorder (SLD)?

While argument still exists over agreeing upon a uniform definition for SLDs, Chapman & Tumner (2000, p. 247) describe an SLD as an unexpected, persistent, and specific difficulty that initially appears in one learning area. They refer to the following definition (p. 241):

Definition 1: The 1977 U.S. Office of Education 
The term "specific learning disability" means a disorder in one or more of the basic psychological processes involved in understanding or in using language, spoken or written, which may manifest itself in an imperfect ability to listen, speak, read, write, spell, or to do mathematical calculations. The term includes such conditions as perceptual handicaps, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia. The term does not include children who have learning disabilities which are primarily the result of visual, hearing, or motor handicaps, or mental retardation, or emotional disturbance, or of environmental, cultural, or economic disadvantage.

(United States Office of Education. (1977). Definition and criteria for defining students as learning disabled. Federal Register, 42:250, p. 65083. Washington, DC: U.S. Government Printing Office.)

If we are to use this, the question then becomes, applying the ‘exclusion factor’, what is an emotional disturbance, and is maths anxiety more than (or less than) and emotional disturbance? By reading further in Chapman & Tumner (2000), they situate SLDs using a broader view that takes into account cognitive and motivational processes. Referring to previous research (Chapman, 1988; Chapman & Tumner 1995a, 1997, they further point out that persistent failure in learning can lead to the development of negative academic self-concepts (p. 246). So maths anxiety could be a SLD if…

Krinzinger, Kaufmann & Willmes (2009) perhaps provide a little bit of clarity. They purport that while maths anxiety is often associated with Mathematical Learning Disabilities, “the emotional aspects often associated with these

primarily cognitive problems are often neglected” (p.206). Interestingly they refer to Lang (1968) who stated that maths anxiety is-like any other phobia-influencing individuals on three different levels: physiologically, cognitively, and behaviourally. These directly parallel the observations I had made of my son and would tend to support our thought that he did indeed suffer from maths anxiety.

However, while this tells me what maths anxiety is, it raises even more questions. What causes maths anxiety, and more importantly what comes first, the chicken or the egg? (i.e. does maths anxiety cause poor performance or does a lack of self concept lead to anxiety?)

References 

Ashcraft, M, & Moore, A. (2009). Mathematics anxiety and the

affective drop in performance. Journal of Psychoeducational Assessment, 27(3), pp. 197 – 205. Retreived from:

http://jpa.sagepub.com/content/27/3/197.abstract

Berk, L. (2009). Child Development (8Ed). Boston, USA: Pearson Education

Chapman, J., & Tumner, W. (2000). Students with learning and reading difficulties . In D. Fraser, R. Molten and K. Ryba (Eds.), Learners with Special Needs in Aotearoa New Zealand. Palmerston North, New Zealand: Dunmore Press.

Krinzinger, H., Kaufmann, L., & Willmes, K. (2009). Math anxiety and math ability in early primary school years. Journal of Psychoeducational Assessment, 27(3), pp. 206 – 225. Retrieved from:

http://jpa.sagepub.com/content/27/3/206

Sheffield, D, & Hunt, T. (2007). How does anxiety influence maths performance and what can we do about It? MSOR Connections, 6(4), pp. 19 – 23. Retrieved from:

http://www.ltsn.gla.ac.uk/headocs/6419_anxietymaths.pdf

University of Waikato

Faculty of Education

Curriculum Development in Mathematics, Science, and Technology TEMS320-12B

Assignment 2: Investigating an issue in a critical manner.

Investigative Question: How might I recognise mathematics anxiety and what might I do to to allay it?

So, why did I choose to research the murky realms of Maths Anxiety?  For me, as a pre-service teacher in my final year of tertiary study, the reasons are twofold. The first is for purely personal reasons. My eldest son will soon be 16 years old, and from a very young age it became obvious that he had difficulties with mathematics. He quickly realised that he was 'failing', and it appeared that no matter how hard he tried the gulf continued to widen. Here, it would be remiss of me to note that as a father who had always found maths easy, I had high expectations that he would have the same innate ability...so naturally, we (I) pushed harder because it was "obvious" that he just wasn't trying! How could he not get maths? It was simple. 

As his school life continued, our son developed what we called a phobia of maths. When still young, any school work that looked or even sounded like maths resulted in an almost palpable physical reaction...fight or flight! This slowly progressed to the point where, as a coping mechanism, when the word maths was mentioned you could hear the shutters being slammed down...followed by a raft of avoidance and deflection strategies. Unfortunately, as parents we, at times, were not as understanding as we could/should have been, and this only exacerbated matters. However, this wasn't helped by the common school of thought that prevailed at the time which situated maths anxiety as an urban myth used as a cop out strategy to explain away laziness or stupidity!

The first reason for wanting to take this exploration is obviously very personal and somewhat cathartic, and it is embedded within the second. As a beginning teacher next year, I want to be in a position where I can readily identify what maths anxiety looks like, what the risk factors are, and how to help allay the effects of it for students in my classroom. I want all my students to face maths without fear -and perhaps with excitement in its stead- so they can all achieve to their true potential.

An Epilogue: My son has made amazing progress of late. Though he will never sleep with his maths book under his pillow, or obtain a doctorate in applied mathematics, he is achieving (in what is an important academic year) through hard work, perseverance, and a little bit more patience and understanding.