Backward 6 Meaning

[Giraldo Allain]

This teaching guide will explain the benefits of incorporating backward design. Then it will elaborate on the three stages that backward design encompasses. Finally, an overview of a backward design template is provided with links to blank template pages for convenience.

In Understanding by Design, Wiggins and McTighe argue that backward design is focused primarily on student learning and understanding. When teachers are designing lessons, units, or courses, they often focus on the activities and instruction rather than the outputs of the instruction. Therefore, it can be stated that teachers often focus more on teaching rather than learning. This perspective can lead to the misconception that learning is the activity when, in fact, learning is derived from a careful consideration of the meaning of the activity.

As previously stated, backward design is beneficial to instructors because it innately encourages intentionality during the design process. It continually encourages the instructor to establish the purpose of doing something before implementing it into the curriculum. Therefore, backward design is an effective way of providing guidance for instruction and designing lessons, units, and courses. Once the learning goals, or desired results, have been identified, instructors will have an easier time developing assessments and instruction around grounded learning outcomes.

The incorporation of backward design also lends itself to transparent and explicit instruction. If the teacher has explicitly defined the learning goals of the course, then they have a better idea of what they want the students to get out of learning activities. Furthermore, if done thoroughly, it eliminates the possibility of doing certain activities and tasks for the sake of doing them. Every task and piece of instruction has a purpose that fits in with the overarching goals and goals of the course.

As the quote below highlights, teaching is not just about engaging students in content. It is also about ensuring students have the resources necessary to understand. Student learning and understanding can be gauged more accurately through a backward design approach since it leverages what students will need to know and understand during the design process in order to progress.

In the first stage, the instructor must consider the learning goals of the lesson, unit, or course. Wiggins and McTighe provide a useful process for establishing curricular priorities. They suggest that the instructor ask themselves the following three questions as they progressively focus in on the most valuable content:

The figure above illustrates the three ideas. The first question listed above has instructors consider the knowledge that is worth being familiar with which is the largest circle, meaning it entails the most information. The second question above allows the instructor to focus on more important knowledge, the knowledge and skills that are important to know and do. Finally, with the third question, instructors begin to detail the enduring understandings, overarching learning goals, and big ideas that students should retain. By answering the three questions presented at this stage, instructors will be able to determine the best content for the course. Furthermore, the answers to question #3 regarding enduring understandings can be adapted to form concrete, specific learning goals for the students; thus, identifying the desired results that instructors want their students to achieve.

The second stage of backward design has instructors consider the assessments and performance tasks students will complete in order to demonstrate evidence of understanding and learning. In the previous stage, the instructor pinpointed the learning goals of the course. Therefore, they will have a clearer vision of what evidence students can provide to show they have achieved or have started to attain the goals of the course. Consider the following two questions at this stage:

At this stage it is important to consider a wide range of assessment methods in order to ensure that students are being assess over the goals the instructor wants students to attain. Sometimes, the assessments do not match the learning goals, and it becomes a frustrating experience for students and instructors. Use the list below to help brainstorm assessment methods for the learning goals of the course.

The final stage of backward design is when instructors begin to consider how they will teach. This is when instructional strategies and learning activities should be created. With the learning goals and assessment methods established, the instructor will have a clearer vision of which strategies would work best to provide students with the resources and information necessary to attain the goals of the course. Consider the questions below:

A link to the blank backward design template is provided here ( ), and it is referred to as UbD Template 2.0. The older version (version 1.0) can also be downloaded at that site as well as other resources relevant to Understanding by Design. The template walks individuals through the stages of backward design. However, if you are need of the template with descriptions of each section, please see the table below. There is also a link to the document containing the template with descriptions provided below and can be downloaded for free.

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when we do d.backward(), that is fine. After this computation, the parts of the graph that calculate d will be freed by default to save memory. So if we do e.backward(), the error message will pop up. In order to do e.backward(), we have to set the parameter retain_graph to True in d.backward(), i.e.,

Right now, a real use case is multi-task learning where you have multiple losses that maybe be at different layers. Suppose that you have 2 losses: loss1 and loss2 and they reside in different layers. In order to backprop the gradient of loss1 and loss2 w.r.t to the learnable weight of your network independently. You have to use retain_graph=True in backward() method in the first back-propagated loss.

This is a very useful feature when you have more than one output of a network. Here's a completely made up example: imagine you want to build some random convolutional network that you can ask two questions of: Does the input image contain a cat, and does the image contain a car?

One way of doing this is to have a network that shares the convolutional layers, but that has two parallel classification layers following (forgive my terrible ASCII graph, but this is supposed to be three convlayers, followed by three fully connected layers, one for cats and one for cars):

Given a picture that we want to run both branches on, when training the network, we can do so in several ways. First (which would probably be the best thing here, illustrating how bad the example is), we simply compute a loss on both assessments and sum the loss, and then backpropagate.

However, there's another scenario - in which we want to do this sequentially. First we want to backprop through one branch, and then through the other (I have had this use-case before, so it is not completely made up). In that case, running .backward() on one graph will destroy any gradient information in the convolutional layers, too, and the second branch's convolutional computations (since these are the only ones shared with the other branch) will not contain a graph anymore! That means, that when we try to backprop through the second branch, Pytorch will throw an error since it cannot find a graph connecting the input to the output!In these cases, we can solve the problem by simple retaining the graph on the first backward pass. The graph will then not be consumed, but only be consumed by the first backward pass that does not require to retain it.

EDIT: If you retain the graph at all backward passes, the implicit graph definitions attached to the output variables will never be freed. There might be a usecase here as well, but I cannot think of one. So in general, you should make sure that the last backwards pass frees the memory by not retaining the graph information.

As for what happens for multiple backward passes: As you guessed, pytorch accumulates gradients by adding them in-place (to a variable's/parameters .grad property). This can be very useful, since it means that looping over a batch and processing it once at a time, accumulating the gradients at the end, will do the same optimization step as doing a full batched update (which only sums up all the gradients as well). While a fully batched update can be parallelized more, and is thus generally preferable, there are cases where batched computation is either very, very difficult to implement or simply not possible. Using this accumulation, however, we can still rely on some of the nice stabilizing properties that batching brings. (If not on the performance gain)

In backward induction, you begin with the last action of the last player of the game, and reason backward from that point. If you can imagine the optimal action of the last player, then you can deduce the optimal action of the next-to-last player, and so on up the decision tree until you get to the first player's first action. Backward induction assumes player rationality and perfect information and works best for sequential games.

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