diff --git a/rest_framework/fields.py b/rest_framework/fields.py
index 460645796..141bf663c 100644
--- a/rest_framework/fields.py
+++ b/rest_framework/fields.py
@@ -678,18 +678,21 @@ class IntegerField(Field):
             message = self.error_messages['min_value'].format(min_value=self.min_value)
             self.validators.append(MinValueValidator(self.min_value, message=message))
 
+    def coerce_to_int(self, value):
+        return int(self.re_decimal.sub('', str(value)))
+
     def to_internal_value(self, data):
         if isinstance(data, six.text_type) and len(data) > self.MAX_STRING_LENGTH:
             self.fail('max_string_length')
 
         try:
-            data = int(self.re_decimal.sub('', str(data)))
+            data = self.coerce_to_int(data)
         except (ValueError, TypeError):
             self.fail('invalid')
         return data
 
     def to_representation(self, value):
-        return int(value)
+        return self.coerce_to_int(value)
 
 
 class FloatField(Field):
@@ -925,9 +928,6 @@ class DateField(Field):
         self.fail('invalid', format=humanized_format)
 
     def to_representation(self, value):
-        if not value:
-            return None
-
         if self.format is None:
             return value
 
@@ -941,10 +941,7 @@ class DateField(Field):
         )
 
         if self.format.lower() == ISO_8601:
-            if (isinstance(value, str)):
-                value = datetime.datetime.strptime(value, '%Y-%m-%d').date()
             return value.isoformat()
-
         return value.strftime(self.format)
 
 
diff --git a/tests/test_fields.py b/tests/test_fields.py
index 1531fe2ac..c1497fb32 100644
--- a/tests/test_fields.py
+++ b/tests/test_fields.py
@@ -563,7 +563,8 @@ class TestIntegerField(FieldValues):
         1: 1,
         0: 0,
         1.0: 1,
-        0.0: 0
+        0.0: 0,
+        '1.0': 1
     }
     field = serializers.IntegerField()
 
@@ -726,10 +727,7 @@ class TestDateField(FieldValues):
         datetime.datetime(2001, 1, 1, 12, 00): ['Expected a date but got a datetime.'],
     }
     outputs = {
-        datetime.date(2001, 1, 1): '2001-01-01',
-        '2001-01-01': '2001-01-01',
-        None: None,
-        '': None,
+        datetime.date(2001, 1, 1): '2001-01-01'
     }
     field = serializers.DateField()