diff --git a/patsy/design_info.py b/patsy/design_info.py
index 2f98968..7cd74a0 100644
--- a/patsy/design_info.py
+++ b/patsy/design_info.py
@@ -685,7 +685,7 @@ def var_names(self, eval_env=0):
         else:
             return {}
 
-    def partial(self, columns, product=False):
+    def partial(self, columns, product=False, eval_env=0):
         """Returns a partial prediction array where only the variables in the
         dict ``columns`` are tranformed per the :class:`DesignInfo`
         transformations. The terms that are not influenced by ``columns``
@@ -703,6 +703,18 @@ def partial(self, columns, product=False):
         :returns: A numpy array of the partial design matrix.
         """
         from .highlevel import dmatrix
+        from types import ModuleType
+
+        if not eval_env:
+            from patsy.eval import EvalEnvironment
+            eval_env = EvalEnvironment.capture(eval_env, reference=1)
+
+        # We need to get rid of the non-callable items from the eval_env
+        namespaces = [{key: value} for ns in eval_env._namespaces
+                      for key, value in six.iteritems(ns)
+                      if callable(value) or isinstance(value, ModuleType)]
+        eval_env._namespaces = namespaces
+
         if product:
             columns = _column_product(columns)
         rows = None
@@ -712,7 +724,7 @@ def partial(self, columns, product=False):
             rows = len(columns[col])
         parts = []
         for term, subterm in six.iteritems(self.term_codings):
-            term_vars = term.var_names()
+            term_vars = term.var_names(eval_env)
             present = True
             for term_var in term_vars:
                 if term_var not in columns:
@@ -1312,6 +1324,16 @@ def test_DesignInfo_partial():
     assert_raises(ValueError, dm.design_info.partial, {'a': ['a', 'b'],
                                                        'b': [1, 2, 3]})
 
+    def some_function(x):
+        return np.where(x > 2, 1, 2)
+
+    dm = dmatrix('1 + some_function(c)')
+    x = np.array([[0, 2],
+                  [0, 2],
+                  [0, 1]])
+    y = dm.design_info.partial({'c': np.array([1, 2, 3])})
+    assert_allclose(x, y)
+
 
 def _column_product(columns):
     from itertools import product