When Link reaches Hateno Village in The Legend of Zelda: Tears of the Kingdom, he will come across the Hateno Village School where Symin teaches. After speaking with Symin, Link will be presented with two different quests of the same name, Teach Me A Lesson which involves Link helping Symin educate his students.
The first Teach Me A Lesson quest in Hateno Village in Zelda: TOTK will involve Link locating a visual depiction of the Great Calamity and the second quest will require him to craft a monster recipe. These quests will need to be done in order as the second will not become available until the first is fully completed.
How To Complete Teach Me A Lesson 1
Upon first meeting Symin at the schoolhouse, he will be attempting to teach the village children about the Great Calamity. Unfortunately, they're neither interested nor really believe it so Symin needs help convincing them. He knows that showing them a visual representation in some way will do the job.
Therefore, Link will need to travel to Kakariko Village and head to Lady Paya's, which formerly was the home of Lady Impa in Zelda: BOTW. For players who have already been there, they will be able to fast-travel to the nearby shrine which is directly above Lady Paya's Hall.
In order to complete the first Teach Me A Lesson quest, Link will need to unlock the Camera on the Purah Pad. This is done by completing a quest with Robbie in the Depths. To start this quest, head to Lookout Landing and speak with Robbie and Josha. After completing the quest in The Depths, Link will have unlocked the Camera.
For those that have not been to Kakariko Village in Zelda: TOTK, it can be found North-West of Hateno Village in the neighboring region. Once there, head inside Lady Paya's building at the head of the village and go straight up to the second floor via the right staircase.
At the top, there will be a screen showing the Great Calamity, use Link's Camera on the Purah Pad to take a picture of it. To ensure that the correct thing is being photographed, stand directly in front of it and open the camera, there should be an indicator in the top right corner to let Link know this object is associated with a quest he is completing.
After Link has a good image of the Great Calamity illustration, he can fast-travel back to Hateno Village and return to the schoolhouse. Be aware that the school day works as a normal school day would, meaning that the children will only be there during mid-day hours.
So if Link returns during any other time period, he can either do other tasks while he waits or he can rest at the nearby fire at Reede's House to the time until Noon. Once the children are in the schoolhouse, Link can speak with Symin who will show the children the image and Link will be rewarded with 10x Hylian Rice in Zelda: TOTK.
How To Complete Teach Me A Lesson 2
After completing the first Teach Me A Lesson quest, interact with Symin again to be given the second Teach Me A Lesson quest. This time, Symin is trying to teach the children about recipes in Zelda: TOTK, specifically involving Monster Extract. The children don't believe any good recipe could utilize this ingredient, therefore, Symin needs Link to help him craft Monster Curry, so he can show it to them. In order to craft Monster Curry, Link will need three ingredients. Hylian Rice, which he will have just received from completing the first quest, Goron Spice, and Monster Extract.
As expected, the easiest place to find Goron Spice is in Goron City up near Death Mountain in the Eldin Region. Fast-travel up to Goron City and there will be a general store of sorts run by one of the Gorons in Zelda: TOTK where Link can purchase Goron Spice among other things.
If the shrine nearest to the village is not unlocked, the best option to reach Goron City quickly is to use the Eldin Canyon Skyview Tower and paraglide in as close as possible and then travel the rest of the way.
While visiting Goron City, be sure to check out the Weapon Repairing Octoroks in Zelda: TOTK which are close by and can fix, and upgrade, any weapons Link may need.
After grabbing the Goron Spice ingredient, Link will need to grab Moster Extract from Tarrey Town. This town is also going to be found in the upper right region of Zelda: Tears of the Kingdom's map. Once there, there will be a small shop with a merchant who sells unique items, mostly that can be fused to arrows, however, he will also sell Monster Extract.
After purchasing the Monster Extract, Link can head back to Hateno Village. If by chance, Link has used up all of his Hylian Rice, he can purchase more from the Hateno General Store.
If low on Rupees to purchase all three ingredients, try heading to any merchant and selling some of the more common objects Link has acquired and can spare. Additionally, the Wells in Zelda: TOTK have Ore Deposits where Link can sometimes find valuable gems he can sell if he doesn't need them for fusing. There is one Well right in Hateno Village.
Now that Link has all three ingredients for the Monster Curry, he just needs to make it. This can be done at any cooking pot, but if having trouble tracking one down, head out near where the little bridge crosses the river in Hateno Village and there will be an overhang protecting two cooking pots.
Use Flint to craft a fire in Zelda: TOTK under the cooking pot and then cook all three ingredients. Link will now have made Monster Curry which unfortunately is not a particularly powerful dish. Take it back to Symin in the Schoolhouse in The Legend of Zelda: Tears of the Kingdom to complete the second Teach Me A Lesson quest.