Why is this important?
Requiring that students stop and bring their ideas or learning to that point to a single understanding means that the students have to process the material or instruction provided thus far and make sense of it. Otherwise, students are left trying to learn the instructor's or author's or expert's thinking instead of making the learning their own. This is a vulnerable state as it means that if a student forgets part of the algorithm taught, steps taught or conclusion provided, the student has no way to build on the learning. By insisting that students consolidate their learning, the teacher provides critical scaffolding to help students internalize knowledge and skills, enabling them to be able to extend, build on, transfer and apply that understanding. Taking the time to have students summarize and synthesize is the key to teaching for transfer.
You might want to start here:
Read through the following quotes to get a sense of the difference between summarizing and synthesizing and the power of each when learning:
1. Summarization is the restating of the main ideas of the text in as few words as possible. It can be done in writing, orally, through drama, through art and music, in groups and individually. There is extensive research that shows that summarization is among the top nine most effective teaching strategies in the history of education (Marzano, Pickering, and Pollock, 2001). Teachers who start a lesson by summarizing the big points in the day's lesson and end by having students summarize their learning see gains in the retention of the material. https://wvde.state.wv.us/strategybank/summarization.html
2. As a learning strategy, summarizing is quite powerful because it requires you to: understand the material in order to summarize it; reread the material or portions of it to refresh your understanding of the main points; distinguish between what are the main ideas that must be included in the summary and which ideas can be omitted; and rewrite the ideas in your own words. http://www.virtualsalt.com/learn3.html
3. Synthesizing takes the process of summarizing one step further. Instead of just restating the important points from text, synthesizing involves combining ideas and allowing an evolving understanding of text. Into the Book defines synthesizing as “[creating] original insights, perspectives, and understandings by reflecting on text(s) and merging elements from text and existing schema.” For students, the site provides the simpler “Put pieces together to see them in a new way.” [...] As with summarizing, this higher-order thinking skill needs explicit instruction and modeling. http://beyondpenguins.ehe.osu.edu/issue/climate-change-and-the-polar-regions/summarizing-and-synthesizing-whats-the-difference
4. Synthesizing information requires a student to process and interact with information rather than simply copying and pasting information. Students are actively engaged with information when they categorize, analyze, combine, extract details, re-assess the value of the collected information, look for bias, omissions, etc. Finally, they related this new understanding to their own knowledge and experiences and develop new meaning or solution. When Debbie Miller was asked how she began to understand synthesis, she replied, “[Y]ou told the kids that synthesis is like throwing a rock into a pond: first there's the splash, and then the water ripples out, making little waves that get bigger and bigger You likened that to synthesis, remember? You said that as you read, your thinking evolves as you encounter new information, and the meaning gets bigger and bigger, just like the ripples in the pond.” https://www.bcps.org/offices/lis/models/tips/synthesizing.htm
See it in action: