Trace back to the whole and coherent development of models on classroom processes, most modern models which categorize the variables or explanations of perse influences on educational processes today stem from Carroll's (1963) seminal article defining the major variables related to school learning. Carroll specialized in language and learning, relating words and their meanings to the cognitive concepts and constructs which they create (Klausmeier & Goodwin, 1971). Carroll’s major premise is that school learning is a function of time. He came up with his model with the statement that time is the most important variable to school learning in The Model of School Learning which has taken its place as a useful guide in research on teaching and learning in schools, especially in classroom processes, since first published 25 years ago. 论文网

In 1963, John Carroll hypothesized that given the right amount of time and appropriate methods, a student would succeed in learning a specified body of knowledge. To be more specific, he proposed that a simple equation for it is:

School Learning = f(time spent/time needed)

Carroll defined management of time spent as a function of opportunity and perseverance. The measure he proposed for opportunity was allocated time or the amount of time the teacher made available for school learning in class. The measure Carroll proposed for perseverance was engagement rate or the proportion of the allocated time that students were actually on task. Allocated time is multiplied by engagement rate to produce engaged time or time on task which is defined as the number of minutes per school day that students were actually engaged in school work. 

And the “engaged time” or “time on task” identified in Carroll's (1963) model has been replaced by Academic Learning Time (ALT) later. To be more specific, as it is presented above, ALT is a combination of three separate variables: content overlap, involvement, and success. Content overlap is defined as "the percentage of the content covered on the test actually covered by students in the classroom" (Brady et al., 1977; Cooley & Leinhart, 1980) and is sometimes referred to as Time-on-Target (Squires, Huitt & Segars, 1983). Involvement is the "amount of time students are actively involved in the learning process" and is often referred to as Time-on-Task (Stallings & Kaskowitz, 1974). Success is defined as the "extent to which students accurately complete the assignments they have been given" (Fisher et al., 1978). 

Carroll’s model boosted the development of the study on the classroom processes. Later, a lot of scholars came up with a wide variety of models about school learning. Among them, Squires et al. model is of vital significance to the improvement of Carroll’s model. One essential addition in the Squires et al. model is the inclusion of school-level processes. These were classified in three categories: Supervision (direct interaction with teachers to improve classroom practice), School Climate (developing the ethos of the school), and Leadership (setting direction and maintaining focus on important issues). These and other variables were late incorporated in models of school learning developed by Proctor (1984) and Cruickshank (1985).

As the development of the school learning models constantly renewed and reorganized, the re-definition of classroom teaching and learning processes were come up with by scholars based on the second language learning. 

The model presented above derived from these and other models related historically to Carroll's model (McIlrath & Huitt, 1995). This system focuses on variables of school learning in four aspects: context, input, and process variables, which can be used to predict changes in scores on a standardized test of basic skills achievement:

Learning (Output) = f(Context, Input and Process).

The interpretation of this formula can be deducted as following: Context includes the environmental or situational factors such as family background and peer group conditions that can possibly influence the measurement and result of certain educational outcomes as well as levels of important input and process variables. Classroom processes mainly contains the thinking, feelings, commitments, and actions of teachers and students within the classroom or learning situation as well as the interaction patterns and descriptions of the learning environment that result from those interactions, and which is widely influenced by the school characters and school processing as the system has analyzed. Additionally, input and output has the interrelationship to each other and output includes the specific measurement or measurements of learning, while input includes the characteristics of teachers and students that they bring to the teaching or learning process.