what grade are you looking at ? are you looking at students with math difficulties, students with math disabilities, or both? 

Whilst my concern is for students in grades 6 -12, the intervention will focus on grade 6. I am using the expression math difficulties in this case to mean anyone who has trouble performing in the regular math classroom, which could of course include students who have math disabilities. Incoming grade 6 students will be identified on the basis of the grade 5 NYS tests as well as a numeracy diagnostic. The school has scheduled those students to do 2 or 3 supplementary numeracy classes each week. Hope this helps!

Hi Martin,

This sounds like a very interesting research project. A couple of questions though.

1. Why do you think that urban classrooms are any different from any other classrooms?

2. How are you defining performance? Performance in rote automaticity tasks or performance in procedural tasks or performance in problem solving tasks?

3. How will you filter out the influence of the various teaching styles and the possible impact this has on performance.

I look forward to reading your findings. Good luck. Kevin

Amongst the 3R in education  ( Reading, wRiting, aRithmetics), it is very much clearly observable that arithmetic inputs need more concentration.

qualitative results can be obtained on these skills.

Sounds very interesting.  I ran a similar experiment in my own classes (6-12th grades) over a number of years after identifying that the majority of struggles in mathematics education stem from students not knowing their basic facts.  As we all know, students memorize their multiplication tables (100 single digit)  but hardly, if ever, do they memorize the other 290 basic facts (+, -, /) .  By simply starting the class with a 5 minute warm up, I found that not only did students dramatically improve on their basics, but their skills translated into higher math efficacy, grades, and application skills.  Granted, my little experiment is not something that is generalizable, but it certainly warrants more research.   Much luck on your dissertation from a fellow grad students currently in the death throws of her own dissertation analysis.  

I'll answer these in the order that they were posted. Firstly Kevin, nice to hear from a fellow Queenslander! I grew up in Southport. As far as your question about the difference between urban mathematics classrooms and other classrooms, My experience in urban mathematics classrooms has been in New York City public schools. Mainly in the Bronx but also in Manhattan, Staten Island, Brooklyn, and Queens over about 11 years. I also worked in non urban schools in areas such as Westchester, Long Island, and New Jersey, as well as teaching math in a semi-rural high School in Australia. The big difference between urban and non urban schools as I see it, involves demographics, classroom size, teacher turnover, socio-economic status. Urban schools have a disproportionately high number of students from minority ethnic groups such as black and Hispanic, and many of these students are from low socio-economic backgrounds, have young inexperienced teachers (who still do a great job!), in classrooms with a high percentage of students classified as special education. Non urban schools tend not to have these features as much.

When I say performance, I refer to the ability of a students to do the mathematics in a regular classroom without being impeded by lack of basic fact recall, and the ability to do operations with pairs of single digit integers.

Finally, you will never filter out the impact of different teaching styles, but will acknowledge it, even embrace it. Similarly every student will have different issues and strengths and we will try and understand those as much as possible. Whilst I am suggesting that there is a link between students' numeracy skills and their ability to 'perform' in the regular classroom, I am not trying to make a generalization or arrive at a preconceived point, but to understand how different students that have been identified as having math difficulties, might be helped by an intervention in basic numeracy, such that they can perform satisfactorily in the regular math classroom.

Krishnan,

Thanks for your comments. I agree with all of you points in terms of arithmetic inputs such as practice, teacher support, and motivation, but often at some point prior to the intervention, some or all of these things were missing. Many of the urban students experiencing difficulty have not had someone to advocate for them.

Thanks Margaret. Some of the teachers that I work with have incorporated a 5 minute warm up or similar idea. It actually becomes a routine that does build student confidence and understanding. Whilst I am not looking to generalize my findings, It is my hope that students who partake in the intervention will be better able to take part in the regular math class.

Best wishes for your dissertation! 

Hi Martin,

I suppose your students speak English as a primary language. In that case you might not have to consider the effect of primary language in acquisition, memory and retrieval during mathematical or arithmetic situations. However, if you have students from different language backgrounds, you  might want to read more about  the numeric system of a language and its effect on acquisition, memory and retrieval. 

Thanks Sospeter,

In New York City our students peak primarily Spanish and English but there is still a significant number who speak other languages. I will look into it.

Martin

  Automaticity is engendered by practice and repetition .

  A common complaint of less able students is that , because they take more time to come to  an answer for a mental task , their peers or the tutor answer the problem aloud without being invited to , this has a significant impact on their willingness to engage further .

  This situation cannot be solved without adequate time being given for a response :  question-by-question silent mental arithmetic tests and time given over to exploring a variety of mental algorithms with graded problems enables students .  This is not usually time-tabled and is the luxury of the able - less able classes get whipped over the course without the extra input needed .

  Automaticity allows for greater speed of delivery , calculation and collaboration - thus ''performance' overall .  Certainly you have identified 'working memory' as the key and recall is the basis of it , but understanding of or having a visualisation of what a written number/computation means is the essential precursor .  It's about literacy first , computational skills come after .  Written Maths uses ideograms , these are meaningless without recognition .

Hi Rich,

I often use the analogy that every musician in a symphony orchestra must know their scales. Having basic numeracy skills is foundational to all higher level mathematics. Another area that is often lacking is problem solving, of which visualization is a critical component. Many of the urban education students that I work with not only lack basic numeracy skills, but do not have a means to solve problems, including the use of some sort of visual representation. We often think of mathematics as being clear cut in terms of its meaning, but a given symbol or expression can have multiple meanings depending on individual interpretation and context. One of my concerns is that students are just learning isolated content without any real connection to their world. They are not building a 'toolbox' that they can use to solve a range of problems both in mathematics and elsewhere. I think that your point about time is critical. Some students just need more time, but often never get to express their ideas.

  Regarding problem-solving , as you say , the main difficulty students face is comprehension of the specific demands in the problem .  This presents initially as a language problem and only after correct analysis can the numerical problem be identified and the synthesis of the solution realised .  Two points here:

a) the language of the problem is more often than not an institutional (formal and using unusual vocabulary and construction) as opposed to the students' own language  .

b) reviewing the problem in print is difficult for the vast majority .

  He solution I suggest is for the students to sketch the problem as they read and re-read , effectively turning it into their own code , visualisation , language, so as to crystallise the essential elements of the problem .  This by-passes language problems and allows review of the information at a glance .  Once distilled thus , the diagram may be manipulated or rearranged to help advance the solution . 

I watched students in a Manhattan High School today attempting to solve problems involving maximizing an area in a rectangle with a fixed perimeter. Almost every student that I spoke to was unable to tell me what the question was asking. Most had not drawn any sort of visual representation. Many had just resigned themselves to passing on the question. I agree that the ability to recode into familiar language is a critical skill, and to draw some sort of visual representation of the problem is another important skill. I think that students need to learn these skills as part of an overall problem solving strategy such as that advocated by Fuchs, L & Fuchs, D. (2001). Principles for the prevention and intervention of mathematics difficulties.Learning Disabilities Research & Practice, 16, 2, 85 – 95.

My study incorporated elements of fluency (promotion of and measurement of) and I developed an instrument that I used to measure the learners fluency in 6 aspects such as bonds to 10, adding / subtracting 10 and 100, doubling, halving. As these were timed tests there were issues with stress but my thesis gives full details or you can look at my Perspectives paper of how i resolved this. 

Article Research tensions with the use of timed numeracy fluency ass...

Thesis Learners’ numeracy progression and the role of mediation in ...

Debbie Sott's PhD study included in her response above looked to some extent at the relationship between fluency and mathematical progression and fluency for progression. We have found in our broader project work with particularly economically disadvantaged communities of SA learners that working with Wright, Martland and Swaffords (2006)  Mathematics Recovery assessment framework, which combines notions of fluency with  progression particularly useful for young learners.

I am not an expert in this area, but two thoughts occur to me from reading this discussion. i hope they have some relevance

Firstly, as the supplement to the question implies, there is no single, easily defined thing called mathematics that we all must master. Mathematics involves concepts and skills, ranging from the very basic to very complex. Only some of us need the very complex, so what do we need? Context also is important. I had school students who seemed to have difficulty in Biology lessons with  both the concepts and skills of adding, subtracting,multiplication and division but showed no problems with these when working on a market stall at the weekend. They could do these (I suppose we see them as basic) skills well in one context and not the other. Creating meaningful (for the students, not the teacher) and engaging classroom contexts introducing mathematical concepts and skills that can also be seen by the students as being meaningful and (potentially) useful has to be part of the solution for both more basic and more complex mathematics, or so I imagine. The right meaningful and supportive context might free up working memory for the more complex mathematical processes. So good luck Martin 

Second, and this may be related to the first, how meaningful are the mathematical problems that we present to our students from their perspective? Why might they think being able to maximise the area of a rectangle is important and not some mysterious thing that they are asked to do for reasons they cannot quite see? Some (perhaps those from backgrounds where  it is a given that whatever education  throws at you must be useful somehow) accept this on trust. Others might need more convincing.