Has strategy become the new algorithm?
Dianne Scouller M A (Hons); M Ed (Hons).
The Numeracy Development Projects are now well established in our schools. Published
reports record measurable successes, but is all really well in mathematics teaching and
learning in New Zealand schools? Are the successes at the level predicted or of the quality desired? This paper addresses some areas of concern about the balance between the knowledge and strategy strands of NDP, along with other related issues.
There is no doubt that the introduction of the Numeracy Development Projects has had a significant impact on teaching and learning mathematics in New Zealand schools. In the early years of the pilot programme there were promising improvements in achievement and understanding levels for both children and teachers, largely through the involvement of designated facilitators. Has the successful growth of the NDP been its own downfall in a sense?
For many decades mathematics educators have struggled to find ways to help children develop the ability to think mathematically, to make sense of numbers, relationships and symbols, in fact to develop mathematical and statistical literacy. New Zealand curriculum documents have recognised this need, for example Mathematics in the New Zealand curriculum (1992, p.11)was very explicit in this regard stating the goals as being to provide the opportunity for learners to “… develop the ability to think mathematically”. George Booker’s (1999) article Thinking mathematically: problem solving, sense-making, and communicating addressed this question in a way which recognised the complexities involved for both teacher and learner. More recently Neill (2008) addressed the same issues and in doing so raised some other fairly common concerns. He argued for a recognition of the need for the learning, indeed memorisation of basic facts accompanied by plenty practice, rather than a simplistic reliance on strategies. There is no denying the value of strategies, since the memorising of decontextualised facts is barren, to say the least, while at the same time strategies are useless in isolation from an acquired bank of knowledge to which they apply.
Here, in theory at least, the Number Framework has it right, with both knowledge and strategy presented as parallel paths. In the first Numeracy Professional Development Projects booklet it is stated: “It is important that students make progress in both sections of the Framework” (Ministry of Education, 2008, p.1). This paper asks the question as to how effectively that partnership of strategy and knowledge is outworked in the reality of our classrooms, while simultaneously raising some other associated issues around mathematics in our primary schools.
At this point a disclaimer is offered. Much of the concern expressed in this paper has arisen from observations of student teachers and their associate teachers during mathematics lessons, along with conversations with several young teachers managing their own classrooms. Should an in-depth, longitudinal research project be undertaken to investigate the issues raised, the results may be different.
One feature of mathematics teaching and learning in the past was the reliance on an algorithmic approach to arithmetic. The four operations were neatly boxed into procedures guaranteed to lead the student to the right answer if every step was followed accurately. Furthermore, examples to be worked through were often at a computational level far beyond that which was appropriate. Anyone born since the introduction of decimal currency in 1967 and general metric measurements from 1975 can count themselves blessed not to have been confronted with working out problems such as these:
£3-14s-7½ or 51lb-11oz ÷16 or + 5
Nonetheless, for many years the formality of this algorithmic approach predominated, leaving behind those who could not understand what was being done or how and why it ‘worked’. Those who succeeded were largely learners with good memories or those who were able to work out for themselves why they worked.
With the establishment of NDP in New Zealand any attempt to revert to such methods is scorned and loudly pilloried. A very disturbing instance arose early in 2009 where a young teacher was severely disciplined by his mentors for daring to write a problem on the board in the form
The intensity and dismissive nature of the rebuke was alarming.
It can not be denied that exclusive use of these traditional algorithms excluded large numbers of children from success and enjoyment of mathematics, so is not a desirable approach on its own. But was that due exclusively to the reliance on algorithms, or can responsibility also be laid at the feet of traditional methods of pedagogy and the prevailing attitudes to mathematics itself? There is no doubt that some mathematicians firmly reject any idea of an algorithmic approach. Holton (2002, p.23) declared categorically that the philosophical underpinnings of the New Zealand mathematics curriculum are in clear opposition to such an approach:
Right at the start we need to say that we do not see mathematics as a set of algorithms that
have to be learned by heart nor teaching as a process of transmitting knowledge.
His understanding is clearly that the formality of an algorithmic approach prevents children from enjoying mathematics or learning genuine life skills, so the emphasis must be on processes and problem solving.
Let’s look for a moment at this word “algorithm”. The Collins Concise Dictionary defines the word thus: a logical arithmetical or computational procedure which if correctly applied ensures the solution of the problem. If a learner is taught to resolve the problem by saying, e.g. 42 +35 40 + 30 =70 2 + 5 = 7 42 + 35 = 77
what is that but an algorithm? Certainly different from the first illustration, and probably considerably more helpful to the learner, but still an algorithm. Or if a problem is resolved by using doubling and halving, is this not an algorithm too? The answer must be ‘yes’ if the above definition is accurate. It is evident that in some of our classrooms the NDP strategies are being taught in the same rigid way as the rejected methods of the past, rather than being presented as a range of possible procedures designed to enrich understanding of knowledge and help build connections.
Despite the ‘mechanical’ nature of algorithms, their very efficiency is an important aspect some mathematicians believe should not to be overlooked. Some mathematicians believe that when algorithms are coupled with understanding they acquire enormous power releasing learners to draw on cognitive resources necessary for deeper thinking (Akin, 2001; Raimi, 2002; Wu, 1999). There is no contradiction in the NDP Book 1 booklet for teachers, where it is clearly stated
Student should not be exposed to standard algorithms until they use part-whole mental
strategies. Premature exposure to working forms restricts students’ ability and desire to use
mental strategies… However in time, written methods must become part of a student’s
calculation repertoire… (emphasis added)
Basic fact knowledge is crucial. The Number Framework emphasises that the process of deriving
number facts using mental strategies is important in coming to know and apply these facts
(Ministry of Education, 2008, p.14)
There is a development in the learning of mathematics from the fundamental skills to more sophisticated ones which is only possible if those basics have been deeply imbedded in a student’s thinking. Many mathematics educators believe that such an approach is the only way to ensure deep and rich learning of knowledge, relationships and concepts.
Teach the grammar of math first: the facts gained inductively through observations of nature.
Then teach the logic of math: the ordered relationships of facts to each other, the abstract
principles and their applications. Students should be given the opportunity to discuss and
debate mathematical concepts… Finish with the rhetoric of math. Let the students
themselves relate mathematical principles to other areas and to the “real world”.
Nance (1996, p.71, punctuation original)
Yet, deep thinking and problem solving skills must not be neglected by aiming only at the refined development of basic skills (Kulm, 1991). The perceived dichotomy between skill acquisition and understanding of concepts is neatly summarised by Wu (1999, p.1)
This bogus dichotomy would seem to arise from a common misconception of mathematics…
that the demand for precision and fluency in the execution of basic skills in school mathematics
runs counter to the acquisition of conceptual understanding. The truth is that in mathematics,
skills and understanding are completely intertwined. In most cases, the precision and fluency
in the execution of the skills are the requisite vehicles to convey the conceptual understanding.
There is not “conceptual understanding” and “problem-solving skill” on one hand and “basic
skills” on the other. Nor can one acquire the former without the latter.
Let the main things be the main thing
So what are the goals of mathematics education in New Zealand? When the first full mathematics curriculum document Mathematics in the New Zealand curriculum (1992)was published, its main focus was on the problem solving approach. A clear rationale was presented, declaring the value of this approach to be the provision of a way for learners to learn to think mathematically, as mentioned above (MiNZC, 1992). By identifying one of the six strands of the curriculum as Mathematical Processes, with three substrands - problem solving, developing logic and reasoning, and communicating mathematical ideas - the Ministry of Education declared its belief in the need for students to develop the ability to think clearly rather than rely on memory recall alone. Similar goals are inherent in The New Zealand curriculum (2007, p.26).
These two disciplines [mathematics and statistics] are related but different ways of thinking
and solving problems. Both equip students with effective means for investigating, interpreting, explaining, and making sense of the world in which they live.
There is little doubt that the goals of the NDP in outworking these wider goals are valid and valuable in acknowledging that a rich understanding of number is paramount, forming a base on which wider mathematical understandings can be built.
One concern raised by Begg (2006) was that of potential overemphasis on number to the detriment of other branches of mathematical learning, despite a clear indication that “It is important that students can see and make sense of the many connections within and across these strands” (Ministry of Education, 2007, p.26). Has his counsel been heeded? Surely rich knowledge and a broad bank of strategies in number must flow over into other strands to enrich the learning in those areas and so to develop a conceptual understanding of the inherent relationships. Has the goal of a deep and rich mathematical literacy been taken captive by the emphasis on building the foundation?
As mentioned above, theoretically the NDP align both knowledge and strategy, but the challenge this paper poses is that in too many instances strategy overrides the development of appropriate knowledge. This should not be a surprise, as for many years now New Zealand has developed its curriculum on the Outcomes Based Education model which values process above knowledge. There is a certain irony in the declaration of New Zealand being a knowledge economy while our schools are consistently reducing content knowledge in favour of strategies and competencies. It should not be a surprise either that in many classrooms the learning of foundational mathematical knowledge has been taken captive by an undue emphasis on learning strategies.
Neill (2008) does not deny the importance of strategy, nor does this writer, but misunderstanding of its role in the learning of mathematics has given rise to the concerns being expressed. When a teacher lacks the very fluency of understanding he/she wants to impart to the class then it is very easy to use the support material as text books rather than seeing them as the source of ideas and strategies from which a framework for lessons can be formed. This easily leads to a reliance on strategy as the goal of the learning, rather than as a tool with which to develop the understanding of the interrelatedness of mathematical facts and concepts.
It has long been recognised that individual teachers have enormous impact on the quality of learning in their pupils. Those with poor mathematical knowledge are more likely to use a rules-based approach whereas the teacher who has a degree of mathematical fluency is more likely to teach conceptually (Shulman, 1986, cited in Brown & Baird, 1993). More recently Hattie (2005) showed from a meta-analysis of a large number of studies that the teacher’s influence on learning is second only to what the learner brings to the situation himself. This is supported by Ward & Thomas (2008) in their contribution to the 2007 review of NDP, where they recommend targeted professional development for teachers. They raise an interesting issue of teachers’ content knowledge not necessarily correlating with pedagogical content knowledge, suggesting even that a mathematically knowledgeable teacher may still struggle with the balance of knowledge and strategy.
Knowledge versus process (strategy)
Mention has already been made of a perception that the knowledge of basic skills and conceptual understanding are separate from one another. A learner who demonstrates a deep and rich conceptual understanding could be said to have developed a level of mathematical literacy, the goal of the NDP. This leads back to the issue of balancing knowledge and strategy in our programmes to give our students the best possible chance to reach that goal.
In exploring the role of memorisation of basic facts Neill (2008) suggests the need for a learner to have instant recall of these facts in order to work on the problem in hand without the need to redirect attention to access the needed facts. The same can be said of strategies. Each learner needs to have a bank, a repertoire of strategies on which to draw in order to maintain focus on the problem needing solution. So it is clearly not one or the other, but a matter of both truly working together, the knowledge being the material on which the strategy operates.
There is nothing new in this assertion, for many decades ago Skemp outlined advantages and disadvantages of an ‘instrumental’ approach focussing on learning facts and rules, and a ‘relational’ approach focussing on strategies. He believed strongly that depth of conceptual understanding comes only with the recognition of the interdependence of the two approaches. “Knowing how [rules] are inter-related enables one to remember them as part of a connected whole, which is easier” (Skemp, 1976, p.23).
There are some who even believe there is still a place for an element of drill and practice to consolidate the knowledge and skills base in order for learners to develop an automatic response. Akin (2001) contends that any hope of developing real depth of facility or even joy in the art of a subject is vitally dependent on the establishment of a deeply embedded foundation. This is seen to be possible only as a result of constant practice and memorisation, despite a widespread reluctance among parents and educators to include expectations of memorisation from children. Although he acknowledges the challenges associated with deep thinking, he also supports the attitude that algorithms and routines are vital resources which children must be able to access almost automatically.
Neill’s (2008, p.19) concern that “Today there has been a tendency to emphasise strategies” needs something added to it, namely, “at the expense of knowledge and to the point of losing sight of the goal.” No doubt many will challenge such an assertion, but again personal observations of many classrooms in a wide range of schools has provided enough ‘evidence’ for this concern to be voiced. Many a classroom of Year Five and Six classes has been visited where children are only just beginning to learn multiplication tables. Would anyone seriously consider leaving the learning of the alphabet this late?
Raising questions about appropriate pedagogy is another discussion which is not new, but one which has been dominated in recent years by reforms which have rejected the traditional knowledge transmission approach in its totality. Certainly teacher-centred classrooms can be lifeless and dull but they don’t need to be, as Hattie’s (2005) findings clearly show. Current approaches to teaching in general, and mathematics specifically have focussed on child-centred, constructivist pedagogy which has stripped teachers of the opportunity to actually teach, making them merely facilitators. This movement is based on the dubious claim that since knowledge is changing so rapidly we need not actually learn anything, but only know how to access it. Consequently our curricula have developed a major focus on thinking skills to the detriment, or even exclusion of memorising and retaining valuable content knowledge. As Quirk (1998) pointed out, such an approach ignores the fact that remembered content is a vital foundation for all understanding and thinking. This belief in the structure and growth of deep understanding was the basis on which Ausubel developed his subsumption theory of developing schemata (Kearsley, 2004).
Rowe (2007) expressed deep concern at professional ignorance of the impact of effective instruction in creating general education effectiveness, claiming that pre-service trainees are rarely taught how to actually teach, but are instead immersed in constructivist, enquiry-based approaches. His plea is for a balanced approach which recognises the strengths and weaknesses of both approaches. He sees the situation where teachers are not effectively using direct instructional methods for the learning of foundational skills and knowledge as an abdication of professional responsibility. Both Rowe (2007) and Quirk (1998) recognised the implications of this lack for marginalised and underachieving children.
In promoting the wise use of instructional methods Rowe (2007) cites a large body of evidence to support his claim that many cases of underachievement are not the results of cognitive or behavioural challenges, but rather a clear lack of actual teaching and academic challenge. His claim is supported by Quirk (1998) who also believes that children from socio-economically deprived areas have difficulties in school mainly because of the shallowness of content which offers no challenge or inspiration. Recent history has provided several examples to support these claims.
In the 1970s and 1980s Marva Collins worked in the ghettoes of Chicago with African American children, who at five and six years of age had been expelled from school as emotionally and intellectually incapable of learning. Her rigorous academic curriculum led to all her pupils successfully graduating either to high school or into the work force (Collins & Tamarkin, 1982). One major longitudinal study undertaken in the USA is worth discussing, because the results indicate clear success from the application of a curriculum model with a pedagogical focus on direct instructional methods. Project Follow Through was introduced in 1967 with the aim of finding effective ways to counteract the negative effects of poverty on educational outcomes. The project ran until 1995, involving 75,000 children in 180 sites, and 22 sponsors who were given the opportunity to prove that their model of pedagogy and curriculum would in fact successfully raise the learning standards of the children in the study.
The curriculum model mentioned above was that which the University of Oregon sponsored - the Direct Instruction model (DI). Their interpretation of the findings of this study have led them to claim that the data unambiguously proves that their model alone consistently showed significant gains across a wide and variable range of sites. This behaviourally oriented model is a highly controlled and structured program emphasising children’s learning behaviour and mastery of learning (Grossen, 1995/1996; Lindsay, 2004). The advocates of DI also claim that children gain significant cognitive and affective benefits along with the development of academic skills and knowledge. Both Grossen, (1995/1996) and Lindsay, (2004) claim that political embarrassment at the success of this model has lead to it being ignored by educational authorities. Although there are aspects of this particular model which could justifiably be challenged, it can not be denied that the focus on teacher lead instruction led to successful learning for the children.
There are several other groups in the USA currently choosing to reintroduce this instructional approach, including one group of charter schools who have introduced a program called the Knowledge Is Power Program (KIPP). This was set up for much the same reason that Marva Collins began her school, namely deep concern at the poor academic achievement levels of disadvantaged children, again mostly urban African-American and Latino children. Beginning at grade five, these college-preparatory schools set a rigorous program of both extended class time and compulsory homework. Rigorous academic work is balanced with extracurricular programs of music, sport and outdoor field trips. In the 2003/2004 school year large numbers of children from disadvantaged homes, who attended KIPP schools, showed extraordinary progress in reading, language and mathematics (Mathews, 2005). There is a growing body of evidence that the methods used by KIPP schools and others using rigorous, knowledge-rich curriculum models which emphasise teacher directed instructional methods significantly raise the academic achievement levels of minority children, dramatically reducing the proficiency gap between them and those in other state schools (Kersten, 2007).
A caution may be appropriate here, as no programme is ever totally successful, and transferring from one context to another raises its own challenges. However these examples, along with the research of the scholars cited above, offer ample evidence to suggest a very strong case for refocusing our curriculum and reconsidering our approaches to pedagogy, especially in our mathematics classes.
This paper is primarily addressing approaches to the strategy strand of the NDP, but that can not be seen in isolation. Numeracy is only one part of mathematics, and mathematics is only one subject of the entire school curriculum, but the issues addressed with regard to mathematics also apply to all other areas of the curriculum. An option has been presented to consider reinvestigating the value of some aspects of a knowledge-based, teacher-lead curriculum model. In particular this paper poses a challenge to those who teach mathematics at any level to reassess the balance of knowledge and strategy/process. Recognition must be given to the importance of evidence provided by decades of empirical research in support of the need for a rich knowledge base on which learners can build a repertoire of strategies in developing the mathematical and statistical literacy NZC claims as its goal. Along with this is the need to be honest about the extent to which current approaches are failing many of our children. There certainly are successes to be applauded, but far too many children are still failing to acquire the academic and life skills necessary for them to move in to fulfilling career paths.
Akin, E. (2001). In defence of "mindless rote", from http://www.nychold.com/akin-rote01.html
Begg, A. (2006). Does numeracy = mathematics. set. Research Information for Teachers, 2, 21,22.
Booker, G. (1999). Thinking mathematically: problem solving, sense-making, and communicating. set. Research Information for Teachers, 2(8), 1-4.
Brown, C., & Baird, J. (1993). Inside the teacher. knowledge beliefs and attitudes. In P. Wilson (Ed.), Research ideas for the classroom. High school mathematics (pp. 245-259). New York: Macmillan Publishing Company.
Collins Concise Dictionary. 21st Century Edition. (2004). Glasgow: HarperCollins Publishers Limited.
Collins, M. & Tamarkin, C. (1982). Marva Collins’ way. New York: G.P.Putnam & Sons.
Grossen, B. (1995/1996). OVERVIEW: The story behind Project Follow Through, 2005, from http://darkwing.uoregon.edu/~adiep/ft/grossen.htm
Hattie, J. (2005). What is the nature of evidence that makes a difference to learning? Paper presented at the ACER Research Conference, Melbourne.
Holton, D. (2002). www.nzmaths.co.nz. Computers in NZ Schools, March 2002, 23-26.
Kearsley, G. (2004 accessed). Subsumption theory ( D. Ausubel), from http://tip.psychology.org.
Kersten, K. (2007). Teach character to cut racial gap in school results. Star Tribune, Minneapolis-St Paul, 1,2.
Kulm, G. (1991). New directions for mathematics assessment. In G. Kulm (Ed.), Assessing higher order thinking in mathematics (pp. 71-80). Washington: American Association for the Advancement of Science.
Lindsay, J. (2004). What the data really show: Direct instruction really works. Retrieved 02/05/2005, from http://www.jefflindsay.com/EducData.shtml
Matthews, J. (2005a, 11th August, 2005). Study finds big gains for KIPP. Washington Post, p. A14.
Ministry of Education, (1992). Mathematics in the New Zealand curriculum. Wellington: Learning Media.
Ministry of Education. (2007). The New Zealand curriculum. Wellington: Learning Media.
Ministry of Education, (2008). Book 1. The number Framework. Revised edition 2007. Wellington: Ministry of Education.
Nance, J. (1996). Worldview test case. Christianity in the math class. In D. Wilson (Ed.), Repairing the ruins. The classical and Christian challenge to modern education. (pp. 59-74). Moscow, ID: Canon Press.
Neill, A. (2008). Basic facts: start with strategies, move on to memorisation. set. Research Information for Teachers, 3, 19-24.
Quirk, W. (1998). The anti-content mindset. The root cause of the “math wars”. Available: http://www.wgquirk.com/content.html
Raimi, R. (2002). On algorithms of arithmetic, from http://www.nychold.com/raimi-algs0209.html
Rowe, K. (2007). The imperative of evidence-based practices for the teaching and assessment of numeracy. Invited submission to the National Numeracy Review, Camberwell, Vic: ACER
Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
Ward, J., & Thomas, G. (2008). Does teacher knowledge make a difference? In findings from the New Zealand Numeracy Development Projects 2007. Wellington: Learning Media.
Wu, H. (1999). Basic skills versus conceptual understanding. American Educator, Fall 1999, 1-7.
Rowe, K. (2007). The imperative of evidence-based practices for the teaching and assessment of numeracy. Invited submission to the National Numeracy Review, Camberwell, Vic: ACER
Ken Rowe’s article is an extremely well balanced approach to issues raised in this paper, as he willingly acknowledges the strengths and weaknesses of both a constructivist approach to teaching maths as well as advocating for a reassessment of the inherent value of teacher directed instruction.
Dianne Scouller is currently the Head of the School of Education at Laidlaw College in Henderson, Auckland, and is currently completing a PhD on a knowledge-based approach to curriculum development. She has been a teacher of mathematics in New Zealand schools since 1968.
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Justice, Mercy, Humility. Three Pillars of Education.
He has shown you, O man, what is good.
And what does the LORD require of you?
To act justly, and to love mercy
and to walk humbly with your God.
(Micah 6:8; NIV)
Some years ago the concept of considering assessment with respect to justice, mercy and humility was presented to me in a document written by Bev Norsworthy. Since then the idea has brewed somewhat until recently when a discussion with a colleague raised the matter again. That sent me thinking a bit more deeply on the implications behind Micah’s words, and the risk of taking verses out of context straight into a current day application.
The prophet Micah lived in the eighth century BC, a contemporary of Isaiah, Amos, Hosea and Jonah. His prophecies were mainly directed against the leaders of both Jerusalem and Samaria. Those who were at the time leading both Judah and the northern tribes of Israel were charged with corruption and misleading their people. The powerful and wealthy were robbing the poor but there was no redress against such injustices. It was as if the whole of Israel had sold its soul. Micah’s call was for them to return to the commands of their God, because they in fact knew what God required of them. There was no excuse for their lack of obedience and outright rebellion.
What possible connection can such a scene have with education in the twenty-first century? A good starting point would be to consider what Jesus Himself said about such issues, remembering that He said He had come to fulfil the Law. That Law required justice, mercy and humility in all relationships, both public and private. Indeed Jesus spoke harshly to those who were hypocritical in their dealings with others. A succinct summary of His teaching is the “Golden Rule’ of treating others as one would want to be treated.
As Christian educators we do well to keep focussed on the teaching of Jesus. How does His teaching really translate into our classrooms, our policies, our pedagogy? We may well ask whether the policies and practices required of us by educational authorities line up with Jesus’ teaching. Are justice, mercy and humility evident in the national curriculum, in teacher salary structures, in school policies, in classroom management systems, in behaviour policies? Should we even be asking that question?
This verse in Micah has captivated my attention, and the more I ponder on it, the more richly it speaks to me, and the more I want to say, “Yes, we should be asking that question.” It was especially relevant for me in the preparation of a teaching unit on assessment and evaluation for a class of trainee teachers. Very useful discussions have emerged on ways to ensure that assessments are just, that mercy is exercised in appropriate situations, and that both teachers and learners approach their work with a sense of humility and service. It is not difficult to extrapolate the concepts to education in general, and even to life itself.
It is worth remembering, that the word ‘education’ comes from the Latin verb ‘educere’ meaning ‘to lead out’. God lead His people out of slavery in Egypt into Canaan, and through the prophets He was calling His people again, out of the darkness of corruption and evil, and into the light of true obedience and worship of the one true God. He still calls us to come out of darkness and into the light of full salvation in Christ. Relationship with the Living God is outworked daily in all we do, and this includes the teaching and learning we call ‘education’.
To explore the subject in any depth may well lead to a whole book, so this brief sketch will do no more than propose thoughts and hopefully raise questions for further investigation and study. There is no attempt to find verses to justify what is said, but rather general biblical principles are presented in the hope that readers will search the scriptures for themselves.
Justice. What does it mean? Is it the paying of penalties or reparations for crimes committed? Maybe society’s legal system shows us this face of justice more often that any other. But what is the biblical concept of justice? It is clearly something God expects us to do. There are Old Testament passages which speak of fair weights and honest scales, of treating people with respect and dignity, of setting reasonable boundaries, both literal and metaphorical, and holding people accountable to these boundaries. Furthermore we are to realise that God Himself models those expectations for us. What we often forget in this regard is the universal law of consequences. Deuteronomy chapter 28 is the best illustration of this law of reaping and sowing.
With respect to education we could ask whether it is just to withhold from children the body of knowledge common to literate society. Some great Christian scholars have declared their belief that excellent education is to be presented in an integrated framework of truth, deeply grounded in Creator God and the creation. Such an education allows for the development of a rich understanding of the associations between all disciplines and roots all learning in an eternal framework of truth.
Whether education takes place in a school setting or at home, these aspects of God’s justice must be in evidence for rich, holistic learning to take place. Teaching methods, learning activities, assessment tasks, behavioural expectations and relationships all need to demonstrate justice as God defines it. Fairness, respect, setting high standards, following through on consequences, both positive and negative, is vital to ensure that learning is enhanced and relationships nurtured.
The outworking of the law of consequences inevitably involves mercy. Without mercy, justice easily becomes legalism. It must be remembered that the teaching & learning relationship is just that – a relationship between the learner and the teacher, and between each of them and God. It’s a kind of three-strand cord. With God’s grace we can find ways to hold people accountable and still exercise mercy. Without consistency and the demand for accountability we can actually do harm. Some might say we sin against the learner and maybe cause them to sin. Jesus had very strong words to say to those who cause children to sin.
This, then, is where humility plays its part. The apostle James cautions us to realise the enormous responsibility and wonderful privilege it is to be a teacher. That might mean in a school. It might mean at home or at church, or in some other environment. But we do well to remember that much (accountability) is required of those to whom much (responsibility) is given. So we approach the task of teaching with an understanding of the genuinely awesome joy and privilege it offers. We will never be truly fruitful teachers unless we learn to humbly rely on the LORD for His strength, His wisdom, and His grace. This does not preclude our own responsibility to learn the necessary knowledge and skills and to develop the appropriate attitudes to fulfil our calling. But it does mean that we don’t have to try to carry out this role of teaching on our own. Humbly submitting to the sovereignty of God will bring the grace to submit to authorities, to treat colleagues and families and learners with respect and to acknowledge that we are but instruments in the Master’s hands. Very valuable and important instruments, but instruments, none the less.
Justice, mercy and humility – three pillars of education, built on the foundation of Christ and His Word.
Integrated Schools have been targeted by the media recently.
The PPTA is going to their AGM with a recommendation that asks the Minister of Education to adopt their draft resolution to have the Private School Conditional Integration Act 1975 abolished, thus stopping any further Integrated Schools. Their primary reasons are theological. Simply, they are against the state funding ChristianSchools.
The second media item stems around the abuse of privilege. The Minister asserts that some Integrated Schools maybe misusing Policy One money and are demanding higher than necessary financial support, which puts a barrier to parents attending an IntegratedSchool.
Both areas are of genuine concern and require our urgent attention.
Firstly, the PPTA resolution is a direct attack on Christianity. It should be of no surprise to Christian organizations. Most are contested for the “prince of the power of the air” hates Jesus and hates any genuine Christ-centred organisation.
One only has to take a brief look at American politics over the last 40 years and you will see how the anti Christian lobbyists have slowly but surely eroded and denied Christian organisations their constitutional rights and their Christian privileges. This is happening in New Zealand. The Christians must unite and lobby with equally aggressive commitment. God does answers prayer and we should be interceding for our organisations. That is one side of the coin. The other side is that we must act with wisdom and with tenacity. Your school needs to be transparent and open to the public. Invite your MP and your local councilors, and those of influence into your school. Seek to win their favour. Hold regular events that brings the public into your school, so that when the time comes you can solicit their written endorsement and support.
The second issue is the use of public money:
Jesus said… “render unto Caesar that which is Caesar’s… and render to God that which is His.” Integrated Schools need to treat government money with the utmost transparency and with genuine Christian integrity. Policy One money is given to Proprietors to assist them maintain their schools to at least a State level. Legislation allows the Proprietors to use unspent money, ie., if the school is up to at least State standard at the end of any given year, excess Policy One money can be used for other projects within the School. The use of this money for non-school projects is illegal. Proprietors need to account for this grant.
Further, the Minister is concerned that there is no barrier to qualifying parents who want their children to attend an Integrated Schools from doing so. The barrier alludes to is the excessive amount of Attendance Dues and ‘donations” parents are expected to pay. There is no question that the Private Schools Integration Act gives Proprietors the ability to charge a compulsory Attendance Due ( which must be approved by the MOE if it is increased) and invite parents to consider a donation towards supporting you’re the delivery of your special character.
Regarding the Special Character contribution, it is over to you to motivate the School community to “buy in” to this voluntary gifting process. The wording in your prospectus is important. BethlehemCollege, for example has just changed theirs from a “Special Character levy” to a “Special Character contribution” to make it clearer that this is not a compulsory charge.
As I close this exhortation I encourage school leaders to re-read the following three documents.
Romans 12:8… We all have different gifts… “if it is serving, let him serve; if it is teaching, let him teach; if it is leadership, let him govern diligently…”
Christian Education Trust’s Ambassador
Often people come into our school and comment that there is something 'different' about it.
PRAISE THE LORD!
Of course there is something different and it is nice that they noticed! There are a lot of differences between us and the schools down the road, but I choose to first concentrate on our teachers.
Lately I have been wondering just how good it would be if staff at Christian schools were paid 10% less than their counterparts in the state sector. Now before you stop reading, I KNOW...I know this may be ridiculous and may not work for many reasons and I also know that our teachers should be worth much more than the public sector (reward in Heaven). However, I have been thinking...
What if we were paid less if we worked in a Christian School?
Tomorrow morning announce to your staff before devotions that the MoE is cutting salaries to all Christian School employees and watch. See who takes a copy of the Ed Gazette with them back to class.
The first thing I look for when I employ new staff is the 'Calling' factor, is this person called to teach in a Christian School. This stems from an interesting situation I found myself in a long time ago.
I had just graduated from Teacher's College and had applied for a teaching position at the best school I could have hoped to teach at. It was the dream job for a new graduate from the Christian Teacher's training centre I had attended for four years.
I got asked to come to an interview and all was going remarkably well until I was asked "How do you know you are 'CALLED' to teach at a Christian School and you are not 'CALLED' to be a Christian teacher in the state sector"? Did I want the job YES!...was I 'CALLED' to the job...I was not so sure.
A teacher or staff member who is 'called' to a Christian school is very different to someone who just wants to work at a Christian School! When it is all said and done, it comes down to accountability. Someone who feels accountable to their Maker tends to be a lot more teachable, committed and reliable that someone who is accountable to a contract with man. I am continually challenged by Matthew 18:5-6 where Jesus tells of the consequences of leading children astray, let's face it as a teacher there is great responsibility and accountability.
So when a new person comes into the school and comments that there is something different about our school, 'it just feels different', I take the time to explain to them the difference it makes in having teachers who are 'called' to teaching (could be as a Christian in the state sector...) and having teachers who come to school on Monday because it is where they work.
As I continue to unpack the NZC I am struck again by the concept of Effective Pedagogy. Not because it is a new concept but rather lost in the guilt of the missed opportunities for students when we as educators get it wrong. At Timaru Christian School our motto is 'Honouring God in All We Do', a motto similar to many other Christian Schools. AND like other schools our motto is not intended just for the students, rather it is to be observed in all aspects of the whole school community. If I and my teachers are to Honour God in our day to day teaching surely we need to be able to develop a model of effective pedagogy which will ensure students get maximum learning opportunities in the classroom.
Our New Zealand Curriculum (NZC) identifies seven dimensions to what it considers constitute Effective Pedagogy;
On the most part, I agree with the above, some more than others, however this is obviously not the only model of effective pedagogy. There are many models around the world and I am sure your school will have a model of sorts, likely to be most clearly defined in the school's Performance Agreements for it's teachers. Whatever the model it does not hurt to ask questions about the source, the relevance and how the model is actually being practiced in each classroom, by each teacher.
The question of relevance is an important question in two ways. Firstly because we are in a time of remarkable changes in technology and secondly we need to be able to relate to our students in our teaching, such as Christ did.
Although the need for Biblical knowledge and knowledge of God will never end, the day of having to memorise menial academic facts, figures and equations is coming to an end. It was going to happen at some time, but already there are countries which are trialling the use of the internet in final exams at the secondary level (ie, Denmark, Australia). If I knew my students had access to the internet during assessments there would be obvious changes to my teaching model.
As Christian educators I am sure that we would all agree that during His time of ministry on Earth, Christ was the perfect teacher. In observing His teaching we see that He was obviously anointed for the job and one of the most powerful aspects of His teaching was relevance. He was able to take heavenly concepts beyond our understanding and explain them through parables which were relevant to the people He was teaching.
Unlike the NZC, a model of effective pedagogy has been developed in New South Wales which has only three dimensions;
The NSW model of pedagogy contains three dimensions: intellectual quality, a quality learning environment and significance. Each component has been proved to improve student learning outcomes.
Promoting high levels of intellectual quality has the potential to cater for a range of individuals that may have special needs or different backgrounds. High levels of intellectual quality have shown positive effects on student outcomes. To promote intellectual quality, teachers need to incorporate the elements of deep knowledge, deep understanding, problematic knowledge, higher-order thinking, metalanguage and substantive communication.
A quality learning environment is important in focusing students’ attention around their learning. By providing a positive and supportive learning environment, student outcomes improve. The elements that promote a quality learning environment are: explicit quality criteria, engagement, high expectations, social support, students’ self regulation and student direction.
Significance is vital in making learning meaningful and important to students. For the work of students to have an impact outside of school, teachers need to ensure that students’ learning matters. Each of the elements of background knowledge, cultural knowledge, knowledge integration, inclusivity, connectedness and narrative must be significant to students, so that they might apply their knowledge in the context of the wider society.
(Summary of the Quality Teaching Discussion Paper)
Department of Education and Training 2003, Quality Teaching in NSW public schools(Discussion Paper),
Department of Education and Training, Sydney
The obvious omission for us as Christian Educators from both the NZC and the NSW models is (understandably) the Spiritual dimension. I have often wondered what this 'Special Character' dimension of Christian Education was called, Spiritual Integration, Bible Knowledge... however in recent years I have come to define it best as Discipleship.
From observations of Christian schools in New Zealand and overseas the only constant is that this Discipleship dimension is defined and delivered in many different ways. I have heard of schools where the 'Discipleship' dimension is delivered purely because the school employs 'good, solid Christian teachers', and in another the Special Character is delivered because the Principal takes daily morning devotions and another where each unit and curriculum plan must 'supported' by scripture. I am not advocating that one school is better than another, rather that we as Christian Educatiors take a close look into the way our school delivers it's Discipleship dimension of the Curriculum and querry whether it could truely come under the banner of Effective Pedagogy.
If we were to combine the NSW three dimensions with our Discipleship dimension, we would have four dimensions which could easily be reviewed at staff meetings once a month. This could be achieved by a short discussion on one of the dimensions each week...OR...use a staff member who you have identified as exceptional in this area and have them present one aspect of what they do in this area...OR...in a larger school management units could be given to four teachers (or shared?) to research and present best practice in each dimension once a month and to carry out 'audits' in classes...(be sure to share this Best Practice on our website!!). The options are endless but there may be no greater task in the school than to ensure effective Christian pedagogy is at the forefront of discussions in staff meetings.