For an R&D institution to design a specific high investment cost product, the budget is usually 'large but limited'. To allocate such budget on the directions with key potential benefits (e.g., core technologies) requires, at first and at least, a priority over the involved design criteria, as to discover the relevant decision knowledge for a suitable budgeting plan. Such a problem becomes crucial when the designed product is relevant to the security and military sustainability of a nation, e.g., a next generation fighter. This study presents a science education framework that helps to obtain such knowledge and close the opinion gaps. It involves several main tutorial phases to construct and confirm the set of design criteria, to establish a decision hierarchy, to assess the preferential structures of the decision makers (DMs) (individually or on a group basis), and to perform some decision analyses that are designed to identify the homogeneity and heterogeneity of the opinions in the decision group. The entire framework has been applied in a training course hold in a large R&D institution, while after learning the staff successfully applied these knowledge discovery processes (for planning the budget for the fighter design works and for closing the opinion gaps present). With the staffs' practical exercises, several empirical findings except for the budgeting priority (e.g., the discrimination between 'more important criteria' against the less important ones) are also interesting. For some examples (but not limited to these), it is found that the results from using two measures (statistical correlation vs. geometrical cosine similarity) to identify the opinion gaps are almost identical. It is found that DMs' considerations under various constructs are sometimes consistent, but often hard to be consistent. It is also found that the two methods (degree of divergence (DoD) vs. number of observed subgroups (NSgs)) that are used to understand the opinions' diversity under the constructs are different. The proposed education framework meets the recent trend of data-driven decision-making, and the teaching materials are also some updates to science education.