Thanks all for your input. Just about all soil in mid-Michigan is pretty much heavy clay which is why I have tried to improve the soil by adding compost and sand, etc. It has been very hot and dry the past 10 days but no matter how much I till the clumps will not break down, I borrow a neighbors rear tine tiller and tried that...still end up with clumps.
What I find so irritating about the clumps is that because where I live there is farmland on two sides of us and the wind comes from those two sides, and because of all the quackgrass and other weeds, any bare soil here is immediately covered with seeds that quickly sprout. Because of the seeds, I have to put down that black fabric landscape ground cover or I can never keep up with the weeds. Trying to pull the weeds from the clumps means they break off in the soil. And the clumps make it almost impossible to level the soil so I can put down the fabric.
As to the original question about "don't pulverize the soil" when I did a Google search about how I could better break up the clumps, many of the hits from Google said "DON'T PULVERIZE" and I could not find out why that was the case. I use a walk behind Rally front tine tiller. No matter how I set it to till shallow or deep, it just moves the clumps around without breaking them down further.