Can i replace the word "lack" insted of "Cuts"!?

Yet many schools across the country have reduced their physical education programs. Criticism of the cuts has led in some places to efforts to give students more time for exercise, not less.

can i change like this

 Yet many schools across the country have reduced their physical education programs. Criticism of the lack of physical educations  has led in some places to efforts to give students more time for exercise, not less.

 does it give the same meaning with original sentence?

please help me ..

i'm very beginner  for english language.....

 Actually lack means deficiency or absence of something needed, desirable, or customary:like , lack of money; lack of skill.