Amdahl's Law specifically applies to the number of computer processors in a system and the time saved by having more processors working. The graph above shows the speedup based on processors for different problem-solving techniques. Specifically, the problem-solving algorithm compares how much of a process is done individually and how many steps can be combined.
The blue line that stops at a speedup limit of 2 shows where 50% of the steps are chunked and 50% are sequential. The number of processors does impact the speed, even marginally, up to 16. Beyond that, there is no speed difference between 16 and 65,536 processors.
The dashed green line at a speedup limit of 20 shows that more processors will increase the efficiency up to about 4096 processors, and then again, there is no appreciable difference no matter how many more processors are used. However, what can be seen is that this algorithm is 10 times more efficient than the 50% parallel algorithm.
Increasing effectiveness combines problem-solving and resources, but Amdahl's Law shows that a good algorithm beats resources. Often, schools and teachers seek the newest great resource to turn around their courses. And having resources is incredibly necessary! An elementary teacher friend of my mother's in southern Alabama was supplied with one ream of paper for the entire school year. Everything else was on her. On the flip side, many EdTech tools seem impressive but have an equally remarkable price tag.
Improving how schools and classrooms operate once basic resource needs are met produces better learning "speedup" than having a subpar teacher given every imaginable resource. Administrators and coaches must focus on Tier 1 and 2 educational practices more than interactive whiteboards and digital textbooks. Great resources can enhance good teaching to a point and can even help mediocre teachers be slightly better. Still, Amdahl's Law shows that a better algorithm (or, in this case, a more skilled teacher) paired with adequate resources is ideal for strong classes.
Leaders must not see this post as an excuse to go cheap or say no to any new resource a teacher wants. Coaches should not discourage the appropriate incorporation of strategically used resources. However, leaders and coaches should seek to improve teaching skills over purchasing resources. If there is a choice between sending teachers to a conference promoting improved questioning strategies or promoting a specific tool, the choice should be the questioning strategies.
When a teacher asks to improve their usage of a specific resource, the first question should not be about the tool but about the instructional goal. Improving the instructional process and then enhancing that with the resource is a more productive approach. The tool the teacher is using may not be the best or is entirely unnecessary. I have witnessed many teachers forcing technology into a lesson that is better without it or being unable to pivot when the technology does not work.
Leaders and Teachers who focus on having teachers operate like a "95% parallel" algorithm will produce better student outcomes no matter how many resources they have available to them. Hire and train teachers to be the best lesson developers, productive conversationalists, intentional questioners, quality assessors, and strongest relationship builders first. Then, provide them with appropriate resources, knowing there is a point where more resources will not make any additional difference. At that point, continue investing in quality instruction to reap the highest returns.
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