Introduction

The Church Growth Model Building Series is a monthly meeting of pastors, leaders and other church workers with an interest in church growth. The aim is to produce a set of models, using system dynamics, that will help church leaders understand how churches grow and decline and help them best lead their churches with a view to producing discipled and mature Christians. The models do not concern the business side of church management but the grow of the Kingdom of God. The series deliberately has a limited time span, so as to focus on the aim delivering working models that will inform the dynamics of church and kingdom growth. The informal meetings are entitled the "Church Growth Cafe", and take place under the auspices of the Cymru Institute for Contemporary Christianity, CICC, in Cardiff, UK, as well as the Church Growth Modelling project, that hosts this website. Summaries of the meetings are also given on the articles page.

Summary of Meetings

Session one, May 2010: How to use System Dynamics to build a church growth model. An introduction to model building in System Dynamics. Notes in the form of: PowerPoint presentation, or as PDF. (8MB files). Use slide show to get the best effect. Homework. System Dynamics Elements.

Session two, June 2010: Principles of church growth. The nature of church and its growth was discussed and written up for the July meeting: Summary 13/7/10. A model of issues raised by messy church was constructed.

Session three, July 2010: Issues in congregational growth. A review of issues that affect congregational growth were discussed following the guidelines: Issues to Consider.

Session four, September 2010: Three working sub-models. The meeting started with a presentation of 3 working sub-models: Discipleship in a modern Conversionist church; Generationally Sustainable church; and Contextual church. These are explained further on the Blog and on the September handout.

Session five, October 2010: Conversionist models. The model was run for the parameter values suggested in the previous meeting. It was clear that the dynamic perception, that is how many were progressing from one category to the next, and how fast, disagreed with the static perception of how many are in each category. A re-calibrated model was also presented. Many suggestions were made as to why the two perceptions disagree. One interesting point was that many of the discipled and mature Christians in a congregation have transferred in or originate as children of believers brought up in church, rather than straight converts. People were asked to re-think the numbers in various categories in their own churches, using the October handout.

Session six, November 2010: Discipleship model results. The discipleship tag is now added to the model. The meeting started with a presentation of the results of the discipleship model to date. Slides on PDF. The model from last time with the expected stocks was recalibrated to show the flows required to produce those values. It was clear that the ideal church with healthy numbers of mature and early mature would required significant flows though and minimal loses. It is felt that this ideal needs to be explored to help facilitate healthy kingdom growth. It was shown how transfers in can also give healthy stock numbers. One suggestions for stock values was shown to be not viable as an equilibrium solution without transfers. There is a danger that many "healthy" churches are either relying on transfers or are not in equilibrium and will become less healthy. Finally the effect of insufficient numbers in the mature category on resourcing discipleship was shown. The next meeting will consider the control viewpoint, i.e. what mechanisms in the church control the flows through the church. Key will also be the process by which potential converts start attending church. The results are summarsied on the Discipleship results page.

Session seven, January 2011: Control of Discipleship. Only the effects of the discipleship loops were presented at this meeting, and that for a 2-stage process only. During the model construction before this meeting it was realised that important issues of supply and demand of discipleship had been raised by the control loops. The mature were need to supply the process of discipleship with the demand being created by the number of believers further down the chain and their expectancy. Unlike market forces a balance of supply and demand is not necessarily achieved. Instead a church could be providing more discipleship than is needed, with the time of the mature being wasted, or more may be demanding discipleship than the mature could deliver. Ideas from supply chain modelling were used to handle supply and demand. A large number of issues had been raised with the modelling of expectancy, desire and how these could be combined with leadership. ideas were taken from current research on modelling soft variables. It was decided that a significant amount of time was needed to finish the model and implement and investigate all its features. the final meeting was to be delayed a few months.

Session eight, June 2011: Finished Model. The model has been finished to 4 levels: Measuring discipleship, resourcing discipleship, controlling discipleship and feeding discipleship. The later two concern the modelling of expectancy and desire. Some issues will need resolving at the fine detail level. The model has been renamed from Conversionist/Discipleship, to simply Discipleship, a title easier to present and promote. The next stage will be to consider an audit tool for measuring discipleship in a congregation and trialling the tool and model on some congregations. Slides for the evening.

The Models

To date 3 models have been suggested in various stages of development:

• discipleship
• contextual
• generationally sustainable

These represent three types of church, although in practice real churches will be some combination of the three.

A discipleship church is one that sees the world and the church as clearly distinguished: unbelievers and believers, unsaved and saved, etc. It will generally have a clear way of identifying itself, such as a main Sunday service that is a reasonable representation of those who "belong" to the church. It will also have additional activities that will clarify who are the committed and more spiritually mature members of the church. Conversion is mainly through an initial contact, maybe something like the Alpha Course, with subsequent stages to deepen the faith towards maturity.

The conversionist church's growth strategy is to see individuals outside the church converted and then discipled to spiritual maturity. Initially it works to change individuals (that is for God to change them) so that they become Christians. Then the church works to develop the converts to become mature followers of Jesus, as the church has defined it. A sociologist might say the church is trying to change people into some church norm, whether intentionally or not. (See discussion on strictness in Kelley, 1986). Essentially it is the individuals that change to fit church, not the church that adapts to fit the individuals.

A contextual church is one that seeks to draw people in from a surrounding community by adapting the church context to the context of society. The contextual church can be split into two broad types, seeker-friendly and emerging.

The seeker-friendly church can be pictured as a sequence of phases, each of which has its own well-defined purpose which can be an end in itself. Each phase can be viewed as an expression of church, some closer to the context of society than others. These phases thus act as bridges between the context of society and the context of church. For example people could start in a Mums and Toddlers group, progress to Messy Church, then further progress to Family Service, then to full Sunday attendance, and finally church membership and communion. Some of the phases may be places of social action some may have a more obvious spiritual element. Although the name seeker-friendly became popular in the late twentieth century the concept is not new. Many churches in the UK in Victorian times tried to "lure" people to church through gentle and more secular entertainment style meetings outside of church. The modern versions have refined the concepts and see the earlier phases as important expressions of church in their own right.

It should be noted that the intention to progress people to the "central core" may not be clear to the participants. This should not be viewed as deceipt by the church, as it could in some cults that use this strategy, but the difficulty the church has in running a meeting which has more than one purpose. They want people to be satisfied with the phase they are in, but also want people to progress to another. Balancing these two purposes may not be easy. many churches know the dilemma of deciding how much challenging spiritual content they can put into a family service in order to challenge people to make a greater commitment, without alienating people from the one expression of church they have been able to relate to.

Emerging churches are also examples of contextual churches, but in this case the definition of what is meant by church is blurred as even the central core of church changes its context to fit society. For example the church in a pub or in a night club might be the "central core" of the church. Instead of phases there are different communities that represent meeting places where Christians relate with the wider population on a spectrum of relationship to Jesus. That relationship spectrum will vary according to the context of the target population. Unlike the seeker-friend they may be no intention to progress people from one community to another. However like seeker-friendly the church community has been adapted to relate better to society

The difference between the contextual church and the conversionist one is that its growth strategy is to change church to fit the societal context with the intention that individuals are included immediately and will then gradually change. Thus the church changes to some degree to fit the individuals rather than seeing an immediate change in the individuals. The degree to which the church is willing to change, and the areas it may change e.g. culture, beliefs etc, will be important issues and vary from church to church.

A generationally sustainable church is one that can sustain itself over long periods purely through the physical offspring of the church members. This is more like church in the Europe would have been in previous generations when there was less social mobility and may also reflect situations today in some non-western cultures. If the birth rate is not less than the death rate and people do not leave then such a church will survive across generations. Some faith groups such as Jews and Roman Catholics could lose people and still grow because there were times when the birth rate exceeded the death rate by some way. Indeed this is the main way most subcultures last many generations.

A generationally sustainable church has no growth strategy other than to survive. It does not seek converts, or to change society, or to change itself to include others. This may be because it believes such changes are in God's hands not theirs.

Real churches may have traits of all three types of church. They rely on the new generation to help them survive, are seeking converts and disciples, and are willing to make changes in church to assist their growth and see the God's mission accomplished. The purpose of the three models is to specifically focus on one mechanism to understand its strengths and weaknesses so that the growth of the church, and the Kingdom of God, can be better facilitated. It should also be stressed that all these churches exist for purposes other than their growth strategy, not least of which is to see God worshipped.

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A Guide to Model Building

Collecting Initial Thoughts

System Dynamics Elements Used in Modelling

Participants were shown how one particular model, loosely based on the Limited Enthusiasm Model, was built. This also introduced them to the concepts of stocks, flows, converters and connectors. The full presentation can be downloaded, with the four elements in System Dynamics.

Essentially there are

• Stocks. Also called accumulations. These measure quantity. What is accumulated stays there unless there are processes that change it. For example the number of people who belong to a church at any given time could be a stock. It is a static view of the system - what is there now, rather than what happens over time.
• Flows. Also called rates. These measure change. How many people are converted per year could be a flow. It is a dynamic view of the system, that is, how things change over a period of time.
• Connector. These control change, though linking one element to another. They capture the sense of cause and effect. If the people who belong to church cause (that is they are involved in the process of) conversion then there is a connector from Church to conversion. The more in the church, the more conversions
• Converter. These convert one type of quantity into another, so that elements of different types can be linked together. Thus they can appear in causal chains. There are special converters that interface with the boundary of the model and have values that are set from outside. These are the parameters.

It is important to understand that any system has a static view (the stocks - what is there now), a dynamic view (the flows - how things are changing) and a causal view (the connectors - what causes what). People possess these three views of a system but often they are in conflict with each other without them realising it. One purpose of a system dynamics model and its simulation is to highlight these conflicts and guide people to a resolution and a better understanding of the system.

Calibration and Parameters

The first model described in some detail was the discipleship model. With the basic stocks of the system constructed from discussions over three meetings the group assigned values to the stocks and to the parameters that control the flows, based on realistic guesses. Thus a static and dynamic view of the system was identified. The causal view was left on hold. A worksheet was constructed with the initial guesses as the parameters. The first guess gave a wide discrepancy between static and dynamic views - note the big difference between the first guess and the second which is where the stocks are calibrated to the flows (attached sheet). Participants were either overestimating the number of spiritually mature people in the church, or underestimating the process to spiritual maturity, or both.

A blank parameter worksheet is also available.

Experiments

Once there are satisfactory calibrations of a model various experiments can be conducted, in the form of "what ifs". For example for the discipleship model one experiment could be "what if there were a sudden influx of converts?". How would the balance of new converts to discipled to mature behave? How long would it take to settle back down?

Causal Loops

With a better understanding of how a model behaves, various control issues can be investigated. This is where causal loops become important, where making a change has an effect which in turn affects the original change. In the case of the discipleship model there are are at least two loops of interest.

1. How does the lack of mature Christians affect the resourcing of the church programme, in particular those resources that help generate mature Christians? Does there need to be a minimum number of mature people for a church to avoid a downward spiral in its numbers?
2. How does the number of discipled Christians affect the quality of the church and the perception of that quality by the people who may be considering joining it? Could a church achieve a critical mass, so that by increasing its fraction of discipled believers, it would have such a positive impact that an upward spiral of growth would result?

Soft or Unquantified Variables

Soft variables are those for which no clear or easy measure exists. In that sense they are unquantified, even though they have an informal sense of measure. For example the quality of the church is a soft variable. There is no easy way to measure it but people have a sense of what is a great church, good church, mediocre and poor. There is quantity but without specific numbers. Most models require such variables.